{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting started\n",
    "\n",
    "[Qiskit](https://www.qiskit.org/) is a comprehensive suite of a language allowing you to define circuits, a simulator, a collection of quantum algorithms, among other important components. For setting it up on your computer, please refer to the Qiskit documentation. Here we spell out the details of Qiskit that are critical for the rest of the notebooks.\n",
    "\n",
    "The most basic elements are quantum and classical register, and the quantum circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.021333Z",
     "start_time": "2018-11-19T19:31:21.244869Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/marshmallow/schema.py:364: ChangedInMarshmallow3Warning: strict=False is not recommended. In marshmallow 3.0, schemas will always be strict. See https://marshmallow.readthedocs.io/en/latest/upgrading.html#schemas-are-always-strict\n",
      "  ChangedInMarshmallow3Warning\n"
     ]
    }
   ],
   "source": [
    "from qiskit import ClassicalRegister, QuantumRegister, QuantumCircuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The classical registers hold measurement results. The quantum circuit takes gates that operate on the quantum registers. Once we define our algorithm in terms of gates and measurements, we need to execute the circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.027087Z",
     "start_time": "2018-11-19T19:31:22.023937Z"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import execute"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The execution can happen on the quantum processing unit or on a classical simulator. We will rely on the simulator, which is called Aer in qiskit. If you want to try the algorithms we construct on the actual quantum hardware, you will need to set up tokens and manage your computational time, since you have a restricted amount of credit each day. This is the main reason we rely on Aer instead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.046301Z",
     "start_time": "2018-11-19T19:31:22.028982Z"
    }
   },
   "outputs": [],
   "source": [
    "from qiskit import BasicAer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This simulator has multiple backends, allowing us to do simulations with slightly different purposes, as we will see later.\n",
    "\n",
    "Qiskit is overly generously with numerical precision, which we suppress for the sake of better readability of the output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.068246Z",
     "start_time": "2018-11-19T19:31:22.048704Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(precision=3, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Backends\n",
    "\n",
    "The most straightforward simulator backend does exactly what we would expect: it runs a quantum algorithm and writes the measurement results to classical registers. After running a circuit a few times on the simulator, we can inspect the statistics of the results. This backend is called `qasm_simulator`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.088792Z",
     "start_time": "2018-11-19T19:31:22.071616Z"
    }
   },
   "outputs": [],
   "source": [
    "backend = BasicAer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us build the simplest possible circuit that has no gates and only a measurement on a single qubit, writing out the result to a single classical register:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.165317Z",
     "start_time": "2018-11-19T19:31:22.091536Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.measure.Measure at 0x7fc66a3b4a90>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(1)\n",
    "c = ClassicalRegister(1)\n",
    "circuit = QuantumCircuit(q, c)\n",
    "circuit.measure(q[0], c[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We execute this circuit on the simulator and observe the statistics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.237384Z",
     "start_time": "2018-11-19T19:31:22.168525Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'0': 100}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "job = execute(circuit, backend, shots=100)\n",
    "result = job.result()\n",
    "result.get_counts(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember that the qubit registers are always initialized as $|0\\rangle$. Not surprisingly, out of a hundred executions, we get 0 a hundred times. If you executed this on the quantum processor, you might get some 1s -- that would be due to noise.\n",
    "\n",
    "If this was the only simulator backend, we would have a hard time debugging our quantum algorithms. Why? We would have to reconstruct the quantum state based on the measurements we make, which is not a trivial task in general. True, this is the only option we have on the actual hardware, but in a simulator, we have one more possibility: we could actually inspect the simulated quantum state (the wavefunction). Qiskit provides a backend for doing this called `statevector_simulator`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.245468Z",
     "start_time": "2018-11-19T19:31:22.240650Z"
    }
   },
   "outputs": [],
   "source": [
    "backend = BasicAer.get_backend('statevector_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, we do not have to add measurements, unless the protocol we are implementing uses a measurement in its internal operation. So we can build a circuit without a measurement and inspect the quantum state directly. With this backend, an empty circuit needs at least an identity operation (`iden`), otherwise a simulation would throw an error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:22.293374Z",
     "start_time": "2018-11-19T19:31:22.248278Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+0.j 0.+0.j]\n"
     ]
    }
   ],
   "source": [
    "circuit = QuantumCircuit(q, c)\n",
    "circuit.iden(q[0])\n",
    "job = execute(circuit, backend)\n",
    "state = job.result().get_statevector(circuit)\n",
    "print(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So in this case, we see it is the $|0\\rangle$ state, as opposed to observing just the measurement statistics. This is especially important because the type of measurements we can perform are extremely restricted: technically speaking, we always measure in the computational basis. This means that, for instance, the states $|1\\rangle$ and $-|1\\rangle$ are indistinguishable based on the measurement statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three handy ways of visualizing what we are doing. The first one is drawing the circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:23.135544Z",
     "start_time": "2018-11-19T19:31:22.296300Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/qiskit/tools/visualization/_circuit_visualization.py:206: DeprecationWarning: The current behavior for the default output will change in a future release. Instead of trying latex and falling back to mpl on failure it will just use \"text\" by default\n",
      "  '\"text\" by default', DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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VYDAYQ0NDp06dojZtR0fHnTt30HdLdHV1mZmZkZcWKEEqlTKZzLHZF6eNzfsJM+4Qi8Xm5uYnTpz4+OOPAcDFxSUoKIjCldkxBs/RMUYBNjrGKMBGxxgF2OgYowAbHWMUYKNjjAJsdIxRgI2OMQqw0TFGATY6xijARscYBdjoGKMAGx1jFGCjY4wCbHSMUYCNjjEKsNExRgE2OsYowEbHGAXY6BijABsdYxRgo2OMAmx0jFGAjY4xCrDRMUYBNjrGKMBGxxgF2OgYowAbHWMUYKNjjAJsdIxRgI2OMQqw0TFGATY6xijARscYBdjoGKMAGx1jFGCjY4wCbHSMUYCNjjEKDNTojx49amtr07eKUSGVSquqqvLy8srKymQymb7lYJRjiEZPSkry8fEpKSnRt5CXIJPJjh8/PmPGDDc3t6VLl3I4HGdn5xMnTuhbF0YJpvoW8BtSqbSiouLnn39OSUkpKyvTt5yXMzg4GB4enpWVhX6cOHFiX1+fUCjcuXNnfn5+eno6nW6Ig4jRYhD/DAcHBzMzMw8Pj+3bt48LlwNAbGwscvnmzZubm5tFIlFpaSmPxwOAzMzMuLg4fQvEvIBBGL2rq4sgCCcnp23btgUFBelbzssRCAR/+9vfAGD9+vVff/21vb09jUbjcDjp6ekhISEAEBsbW1tbq2+ZmP9jEEYvLS1tb28XCoV8Pt/T01Pfcl7OqVOnJBIJk8mMj48fHqfT6QkJCSYmJhKJ5JtvvtGXPIwiBmF0V1dXFoulbxVqkJaWBgB+fn5Tp06Ve4nNZvv5+QHAhQsX9KAMowKDMPr4oqamprGxEQDmzZuntAKKCwSC8bJCagxgo6vNw4cPUUGV0d3d3VHB8FdIjQfdLi8+e/bs7NmzOTk5dXV1/f39Tk5OLi4uUVFRXC5Xp/2OHj6fX11dDQAxMTG2trajadLe3o4Krq6uSiuQcfw8ajjoyuiDg4OHDx+Oi4uTSCRksKur6/Hjx1evXvX39//pp5901LVaZGRk3Lx5EwCioqJGafTOzk5UmDBhgtIKFhYWqNDT06O9Qgwl6MToPT0977zzzu3btwFg/vz5PB6PzWa3t7fX1dWlp6fX1dWx2Wxd9Ds2kEZnMBhKK5iZmaECNrrhQL3RJRIJcjmTyeTz+R988MHwV//85z8nJye//fbblPerGQcOHIiKigIAe3v7UTbp6OhAhZcaXSQSaS0QQw3UG/3AgQNoLL9w4cKaNWvkXmUwGJ988glVfYnF4r6+vkmTJmmcISAgQINOUUHVES4yPnzaNnq+++67v/zlLxo0pBaCIADg6NGjBw8etLGxaWxszMjIKCgo0K+q/v7++vp6V1dXGo02+lYsFotio9fW1h47dgwAVq1apehyCikpKYmOjr5x44ZMJmOz2TExMdu2bdNdd8OxtLREBdLxcpBxa2trDfJPnTrVx8dHM20UIpPJiouLZ8yYIZFIHB0dm5ubp0yZondhvb29DAbDx8dHLaNbW1tTbPT4+Hg0jH322WfUZh7OgwcPAgIC6HT6nj17WCxWVlZWVFRUQ0PDF198obtOSaysrFBBR0ZftGjRokWLNNNGIWKx+PTp0++///7HH38MAC4uLgEBAUlJSfrWpSFUGl0mk126dAkAvLy8Fi5cSGHm4RAEsWnTJolEUlhYiFay9+/fz+Vyjxw5EhYWNmfOHB31S0IaXdWzZlNTEypoZnQDgcFg7NixA+3yAsCWLVv0PpxrA5VGLy0tRXuBHA6HwrRyPHz4sKSkZMeOHeR+jYmJSXx8vLe3d3x8/Pnz53XXNWLy5MmoUF1dvXjxYsUKaGEeADR7eMjPzz958iSaIuudQ4cOlZeXOzg42NjY/PLLL6dPn9avnr6+vqdPn3p6eqo1dbG1taXS6P/5z39Qgdwa1AU5OTkAsGLFiuFBLy8vOzu7/Px83fVLMnfuXFSorKxUWoE0umYfL11dXbW1tYZzWamlpWVoaIhcVNUvAwMDz58/r6mpUcvovb29VBqdvGqgavJKCdevXwcADw8Pubi7u/vt27ebm5sdHBx01zsAcDgcJpM5MDDw4MEDpRVKS0sBgMViubm5aZA/KChoXJxVHl9QedZl9uzZqKDTyxNoBjx9+nS5uLOzMwAIBALddY0wNzdftWoVANy6dau1tVXu1fr6+nv37gHAu+++q9aog9EpVBp95syZ06ZNA4ArV66Ul5crVnj06FFycrKWvXR1ddHpdBMTE7k42pDv7e3VMv9o2LBhAwAMDAzInUcHgEOHDqHpdWRk5BgowYwSKo1Op9OPHDkCABKJZNmyZZmZmW1tbf39/VVVVWlpaSEhIV5eXk+ePFFs2N7e/uv/IHcTlQYBoLu729RUyYwLBdXdjAwNDXVycnJycqqrqxt9q6CgIHQuLSEh4euvvybjycnJ6HEtODjY19dXLSUY3UJQikwmW7lypaq+rK2tL126pNjqpcvGMTExZOXJkyfT6XTFJFu2bAGA7OxstQT7+/ujLqqqqtRqWF9fT9668Pb2Xrt2LTkjZ7PZTU1NamXD6BqKz6PTaLQrV67ExsbK3Rh64403jh07JhQK33vvPS27mDRpkkwmGxoakosPDg6Cpit6GjB9+vTi4uLAwEAAKC4u/vbbb9HjwYoVK/7973/r+oEYoy40QjfrtUNDQ2hZ3drams1mj/7I1EuZP3/+/fv3q6urXVxchseXLl2al5dXWlqq01V8RX755Zfc3NzW1lZHR8fAwEBy8RFjUOjK6LojIiIiLS0tJydHbind3t6+u7u7ra2NPA6OwZCMv6t0wcHBAHD37t3hQYFA0NLSEhgYiF2OUcr4MzqXyzU3Nz9z5kx/fz8ZRIeNVq9erT9dGINm/Bndyspq3759z549Cw0Nramp6e/vT0hISE5Odnd3l7vkgcGQjL85OgBIpdJdu3alpKSQ4j08PK5cuYI2RzEYRcal0REVFRW5ubkikcjT05PL5eIv9cSMwH8BrLo2cw3GhR8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=248x122 at 0x7FC66F9009B0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.tools.visualization import circuit_drawer\n",
    "q = QuantumRegister(1)\n",
    "c = ClassicalRegister(1)\n",
    "circuit = QuantumCircuit(q, c)\n",
    "circuit.measure(q[0], c[0])\n",
    "circuit_drawer(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a quick sanity check to see whether we correctly implemented some circuit.\n",
    "\n",
    "The second one shows the operation on the Bloch sphere, which is especially important for beginners to understand how rotations happen. Qiskit has a built-in function to plot a state on the Bloch sphere. This visualization method relies on the state vector simulator backend. For instance, let's compare the initial state $|0\\rangle$ and the Hadamard gate applied to it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:24.105595Z",
     "start_time": "2018-11-19T19:31:23.142061Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial state\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bns8sCCmVtXqdQNMoViqUy2Wq1eoo77uJ0Y5i8TuEaZpcuXKFWq2GEQRUCgXGpqcpF4ux+mG0kkopabXbIASVUmndjUwYbHRsIOV69Fj9RPtZIQQpFbgyUilShhEGgSCeBGzHwex0wsBPq8UvfvlLnjpyhMmpKVzfR9N1qtUqzXYbpGRqcjJ0qTsdOqZJs9Wi3mwyPTXFZLW6IVCkGwaalEi1mkaTvZQSx3VxXTfeX5uWBZYFhEZ87Ngx3n33XcaqVcbHx9c/O2CkUkxOTNDudGjVarQaDbrdLhVlwP2KkiOMjHbbcF2Xixcvsry0RAqYqlSYqFYpFAo9LiwoNhJgdbt4nkepVApdSQUpZRxs8jwP23Gwu11ctZLqmoaRSpEzDDRdx9D13pUvvEj8/na7je/76IZBq9Xi008+4YUXX2R2epra2hppZYCpVIpKqUSr3abT6VAsFCgWi8ggYPn2bcxuF7PT4XK7TT6bZbxajfffPdTIJNtKynCfm8n0uNaOmnhclT8+ePAg7773Ht989VVyuVy4x1Xn0DSNktpPN5tNlq5fx1RjnJiYIJtIRY0wMtptYW1tjXPnzhGYJjPVKnMzM6TTaYKI8KAe4qRhBVJiWhapVIpMOt2zj414xbbj4Kt8bCaTIatp4SqqjDQi/fdDAKjzW5aFruuUSiVuXLvG+c8/57XXXmOsUsF13XA1XuuCOp9hGFTKZVrtNu1Oh3wQkM1mw+BUJkO5VKLVbNJotbh56xYpw2C8WqWSWPXiVZa+fa76res6OV2HyIiDgHK5zK1bt1hYWGBqehpNiDiCrRsGAshls2iaRqPRwGw2cUwTs9ViZteukW5VAqM97SbwPI9r165x6/p1MrrOvj17GCuV4vSKv0nk1LQs2p0OY5UKhmEQBAGO49C17TBVArFBp9NphKaFPOME/dBXx8VQrrCnKIS+75NVwa4b16/zyaef8sYbb5BXwa5OvcXS//YO+dsOx1+G79h7Kf1n34gLCdrtNo7rUiwU8H0fs9tlvFpFU6yndrtNo9XCcRyErlOtVKhWKrHXIFVFELBhH5xE9Nri0hIfffQR3/rWt+g6Do7jAOFEks1kyKTTBIDrODRaLZAyzEfrOtO7dzM9Pf11ClKN9rQ7Rb1e59qVK3TqdcZLJfbu2UMqlQpXVsUDHmSw0epjWhaGruN5Hh3TxFXBmpSuU8znSafTMYEBlU4RaiXzVS5WKnJDzDyKaIuWhZZgPS0uLvKLX/6Sb73+Ovl8Hghd9Pq//wDRcdDUut398BqZZ/eReXwGpKRYKtFsNml3OuHEoa4hVa64VCpRKpXoWBaNep3VWo2VWo1ysch4pYKmXNwegx2wCESvzczMkEmnWVlZYffu3QRBgG3bdG2bdqdDp9OJg1hlNTYJGEKwcOUKZrPJvgMHerYaX0eMjLYPnudx48YNGisr+LbNrpkZZqam0HQ9jrYmecARogdXCIFlmrFr7AUBhqZRUPs4PcqPqlVTQlh2lziXJgS+piESrrGn0ku+75PJZCjk82iaxurqKidPnuSVV16hlHAhg2aX7kKdlN87sZhvnwmNVo23XCrRaDbpdDpxUULPaiYlhVyOQi6H7TjUGw3qjQartRrVapWJanVDsCgyZNSKHv8deOKJJ/jkk0/YvXs3mq6Ty+XIZrN4vh/mmB2HruOgCUE2l6NrWbieRy6bZW11Fde22X/wIJlcbidf60OFUWgugW63y/nPPqO9skLWMJiZmmJ6cjLOR8bBF9jgtkYMpk6nw63lZTzPI5/LMVYuM6aI8/F5ICZPbHD3FLFBV/tkKSWWZdFoNAikDFc/FaluNhq8+957vPCNb/REZQGaPz0bBon6tsTutRrezbXE5QTlUgnDMOiYJl4ifRPlW6MJJZ1OMzE+zpwiQ9TrdS5fu0az1eq5RlTzG1Eeg4iOCczMziI0jYWFhfV7p6LjxWKRiWqVcrFIoD63JAwCBr5PPpul3W5z+fx51m7f3pDT/rpgZLQKpmly8dw5dM9jolKhVCwyVqmQSqUGEh5QJXBR1UvHsqjV6zSaTXRdZ3pqilKxGK+scbBqmEut/h29Gh3XabcxFWmjWqmQUflL0zT52fHjHDt6lJnZ2Z5z+Q2LzskrAGgb41h03j7bk3aKXG0BNBuNkJWVGI9QdErP85BSks5kmJmaYnZmBkMIlpaXuXrjBl21R11/c1jkEAXOIpf/0OHDXLx4cd2Vju6l+ty5bJbxSoWCIlq4rkut0QhX33Qay7KoLS+zfOMGvppkvk4YGS1hQObKhQsYvs/s9DRoGvlcjkwmM3Q2F4RR0Xanw1q9jmVZpNNpctlsyDRSaYrNwibxufvcSAiDUI1mEzcIKJVKlCuV2A3tdrv87O//nkcPHWLvvn0bxmX+3YU42KUPGL796UK42iYMN5VKkS8UCKSk2W6vc54VKyoZ/Y7elctmmZubY7xaxXMcrl+7xtLt2/FqvT6o9QlOAHOzs6ytrdG17VA2JwhCA07ksYWmkctm4+BXEAQsLC/HKhyWZWGbJkvXruHY9iZ3+eHD195oG40G1y5cIBUE7NuzJ37YI7phkkQQIZCSdqdDbW0Ny7ZJp9NUx8biKGwyBzkMSVvqP9b1POqNRpgqKRbjPGX00H/44YfM7trFIdUlIDqXlBK/0cV67zK+LtECEEOmjc7bZ3uCRkIIdCHIZjK4rkuj2QyLEyJ3PvpRe/EImqZRKZfZs3s3xWKRZrPJ1evXqQ9qS6KMN2UYTE1NsXjrVvjnaBVWSh0yUTes6zqFQoFds7OkUikazSaO49Bqt8NIvOuydP06Vl+/3YcZX2ujXVtb4+alS6SEYN++fWi6juO660XkJMri1P87lsWaMtZsJkNVudKapmG7LgFsWnYWucKxAfTBdhwaKmpaKZc3CKydO38e3/d5+qmn4r8lz9L56TkC28GTAZoXRoMDPwj3lonqIOuXN7CvreIn5WyEQNN18vk8ruvSHbCCRVHu/gVc13WmJieZm53F0HVur6xw9fr1jS6zupd79uxZ39duuElyXV5HBeMymQwTiqmVTqdxXJflaFUPAm4vLNA1zcHne8jwtTXa1dVVrl++TEbX2btnD7oyWCAmQySDT77nUa/XsUyTTCbD+NgYxQR1UQiB6zhxUGUQBkVUkzAti1arhaFpjCXyofGYV1a4cOECL774Yo9rGyFodumeuEygC9AERhgKBk1VDfUsmWD+zblYngbWWU+5bJZMKtUTmEpCqL3qoPRONpNh965dTIyPh3nuGzcGrrq75uZYWVmJq5r671PPX5TxRhF4TdOoVqv4QUC92cQ0TQgCVm7dwv0auMpfS6NtNpvcuHaNUibDvr174+oUz3XRVfQ26oMjgY5pUm824+htpVTqMdboOMdxyKTTG4sB2Hx1jTjKppoQylFhQQKObfP+++/zjeefH0rrs05eRbo+UZZnUBAqCfvMAkF9fXWKotUAxWIRXddpdTrxPrIfQhv++JRLJXbNzZFNpbi9ssLC0lJPbyEjlWJiYoLFpaX1+xJ5N8NYYEAhm8ULAjSgWCigaxpmt0uz1cK1bZYXFgZONA8TvnZG6zgON69epSAEe5IiZLJX71cIgasqdLqWRVbtWzPp9MZcJmFawg+CoXrBw1bXWM3CtsnnchSLxY3HSskHJ0+yZ+/enkjxhnOthvu6QAuvp20jI+KtttfHKAQogxGaRlHxqjub7Bc327unDIPZmRnGymU67TZXr12j2+3Gr+/es4eFmzfXz0W4v/UGGG2ETCZD2jBCJpaiQpYKBTzPo9FqYXU6LN+8+VAb7tfKaIMg4PqVKwjPY3Z2dj2o0pd6iKLCUY/XcqUSusKJnGUk9xIhekjSfUYrN3GHI4P1PC+MOCs2Uz/OX7iA67ocOXJk6GeTQObJ0KB9bfMgVAStmCW1b2LdPU58PlAR5VwOp29/G7nR8f8TLvaGayhXdmZqCikl1xYWWFP3dXpyklqt1nN8QFgw0T+WJHLZLIFKBQWAkU5TqVTQNY1Wu02jVmPx2rWH1nC/Voyo5YUF3E6HyWo11FOKCA6K5aQpcW7bcQh8n6zS/I2IE/151qQ76XneuqJD9DrDV6IgCGi2Wvi+TykSYRuA1dVVzl+4wLfffHPLiHT6qd2U/9NvYJ06j9bxkKs20vYIxLogm1bJoWUNUrMVCm89gZbS1/PEasJKIpfL4bouHdOMpXGiz5ZETLUcMrZ8Ps+cojCurKxgWRbTk5O4nodt22QymThaHUEjNOL+a2XSaXQhaCvmlFDpomKxSNe26Xa7OCsruK7L3kcewXjIanO/NkbbWF2ltbISspTGxgBliIl9mWmadG2bSrlMpVKJA0rRA92/mkSyLFEtrJEIHG2Vn222WmHZXrG4wWCjVJPjOJw4cYKnn346VPvvdmNeclRhFKlAREEu/5EC/uQh0tks1l+dw/38dhgxBlo5SfGtQ+iHJvGApvAR9XpMFrEsK5x8NC0ssFf50nQ6HVIYm02qY2PrK2H/XndIcCpCyjDiHG292eRat0uxVGKtXmd6enrj3lkItMT9SE5amUwGv14PhQPUdTVFzDAMg06nw2qthu957Dt8+KEqqv9aGG231aK2sIAuBLNTU/HfI8J/tOp5nodhGJTL5VC2lARTacgqF+0DI07wMCmZCFLK2CUuFApouo6tjDEpJyOl5NzZs5QrFfL5fM++MhpbtLInVyPheWTSafL5PJrU0V2QUiCQpB3IGinS2WxPbhdFNYyCa77vE/RV70jfp2WadB0nlnzVlF6UHiloRMJ0W6BarZLN5bh9+zZSCG7cvMnk5OTQ4yMPJ0hsNaKJw1PjTN5zQ9cpFYu0Op0w333+PPOHwonsYcBDb7S+ZbFy8yau77N7dhYtmUYRIgxgNJtIKamOj2OZJq7romUym7q3SXieh0ZYwTMsOux6Hp7r0my3sSwrNPBOZ50JJCWaMoBMOk290WBlZYVvv/kmGfWw6QPOH62wEaxuN3S5i0UkOnjrD3vGE2SN9FCyvRBha5GkQmIkKyODACOVwrIsDCXS5noevm337m8JtxuxMFykNtmXvspls+yam6NWq3FraYnVtTUmqtVN73PykzuOQz6bJZAyFABQ54/40rquUy4WqTebNJpNrnz+OfsOHCA7JG7wIOGhNlrfNGmvrWF2u0yMj4cPv1gPzzi2HcvBlJW6RFQqltnmrCyVa4ymkVIumOe68YrpqnYaUb8e13UpFAoU8/nYSHUlCB4ZpOt5/PznP+eZZ56hMEC5sW8AvZ9ZyZreiUzLoOlJ07QwWqnrVCoVJKEyRblUWheck6GGVCQCl/QYuonCiMiADV0PC9+FYP++fVy+epW1tTWCIGBqQO/ceHzq/nhKO6tULMYxiHxiIhKJSbCkWFr1RgN54QL7Dx9+4A33oTVa37YJul3qjQa6CDWaJOvhcsuyaKvgSqVUAlWEns1kME0TRwVHNkO017JUSVmr1QpdW7U6oR7UXDZLt9slm80yNTFBbouyss8vXCCTzbJnz54tP2e/O55cdXaKKCA3DJqmkc/nabfb2Iq+CcSicv0PU7QKer4fC8JZlhW3GTHUhBV4HulUinq9ju/7TE9ObjrpmKYZjiWbxfO8kMXWf08ThhspdTTaba58/jmHHn/8gQ5OPZRGG3gegWnSMU1sx2FqYiKsh1UPS1t1hEurYuuoUgchyOVyYXeATieWftlw/kgl0XFCHd9GA13X8YKAdDq93k5D18MKoE6HIAgo5vNbGmyn0+HsuXO8uY1o8aD9s+/7dx50SfCsh107m8lg2zZmt4uRSg1V7oDQmIW6D1KlwnzV/ycyZMd1yeXzWN0u6VSK1VoNx3HYPTc3cPLpdrs4rkshnw/vs6r6GTRmIURYkywExUKBVrsdcqMvXuSRxx57YEXjHjqjDYIAX7F4Go0GuqZRUmVnfhDQarVwPI98NkuhUFh/o1oZhQh7t641GrQ6ndioIwE213Fi7SVd18OgTy5HLpcbKEIeudvRMZtBSslHH33E4UOHKG7lFrOR7helTL7QSsvmRguEtbSNBqZpUkzew00QdSgQQsTqFBFKSlyuXC4jIRR9b7fZNTtLLpuNVT5836djWaTqFB6mAAAgAElEQVQMI66iyqTTWLaN67qDJyv1OTSlo9Vut1lZXcW4fJn9fZKuDwoePqNVPFRTNbmanppC17SYpxqoIE3U9yau4kk8pLphUMjnaTabdC0LwzDi43Rdj8v2Iu0nq9vtSfdEiPKbmXR6fYKQcmDuEeDmwgId0+SFF17Y1mftP0eUY9XvcAXpF6cbBkPXyWUyoYyOajvSjygNFd03TUV/ByGfz8f56mKxSCGf5/bKCjdu3WJyfDxe0R3HwTAMigmFjpSSdh1qtH2fr1gs0m63Wbx1i1yhwPQmDLP7FQ+mfzAEvmUhHSdMqzQa8X7VV8wjGQRUyuUeg+0vNQuCAMuy6Ha7uEql31HBo/FqlbFKhUKhEJMMYkPpM9ogCGi122jqQYkRke3Vv6Mru67Lxx9/zDPPPDPQJe/HoL1nJHa+nfcPQhQt344eRD6XQ1dqF3E3PZU68qOIc98Yh7mjuVwupjcKIahWq+zevZtcJkPbstBUXrtjmqGus2XhqO9ZCIGRSsWC6UkMkrbVlKuc0nWuXLxIq9nc9v25X/DQGK3vOATdLghBu9XCcV2mJibCom61wlbK5djYki5gQJhCaLZa1NbWwpyoEExMTDA3M0PKMHATD0kSkdH27O2iayqXb5CrGa1qmnLJP/vsM6anp5nYJHq65T1I6CbfEaLih02CUcljC7kcfhBgdrthBHmAoW5828Z7kVWBuiQK+TzTU1MEnsf1xUUymQy7ZmcpqJhDo9WiVq+HTK2EbtcwOmVy3JHhCuDi2bOxouSDgofCaH3fD91iCA2m3SaTSlFQ4X7f9ymXy6Qj9UBlfDII6JgmtVqNZrOJq4gDY0otIaf2vZGoWaPZ3PAFR0abZFa1Oh08lRbZzv7SsiyuXr3K0aee2rAa9a8W8d8HnCdQkeMvIjM6jEccUR2j1VQGQRxwiwJB2z1///iy2WzYriR5PeVe53M5dMIAnaHrFPJ5qpUKxUIBTQg6KgvQUp0SosrD6ByDIAm9kWKhgGPbXDp3bltjv1/wUBitNM2Y+O+o9hTlcjks1/I8iqVSTOSPJU5Nk9W1NTrtdhisKhYZVx0Dkp3LpZRkcznGFOGg3mjELiEQ79Oi1c1SXevyqvZzOzhz5gyPHDhAVjGVknpS/YUJ0Zhi+mLiwfSD4I5X2eQeVPS5u1GAK6ZLsh4DyOdyCCE2rJSboX9iyGazdFUbEQgn4Va7TdeyKBYK7N2zB6QM5WaULnQmnaZSLjOuDFh6Hg2lFGm77vrKO+z6UpJKpcjlctTX1riVqDa63/HAG23gOMhIQVCIsCA6MmDHoVgokFUBCl/tV1drNdqmSTqVYmxsjEqlQiaTGcw2UudNpVKMVSpks1lM06TeaOCowgJ1UBh46nRIq4dhO2i32ywsLPDo4cPhaQYckzTi6IFP/j8yJt/3YxlUCRAo4w5krAIhkT0GGgeL+vb2SbG5zVzOqDm2bdtDjWQQtD6jtbpdpJR0u11a7TZBEJDP5ykUCuTzeSYnJnBsm0VluPF5lJ7X2NgY6UwmzhDUm82YDjrghsaeUS6bJZ1KcbOvbPB+xgNttFLKcB/LOn3NNM1QdtP3KeTzYRmXXNd0Mi0rlIkplykp6dBh5w5Puf5wRT1nSooN1FDtM3wlTjYw8LQFPj1zhkNfkNAuhIgnD121FAnphJGBa70FD0N+i/UT7uj6WcU0GyRPsxkiwzUMg0B1q7dUtL6UaLsJYZqpOjaGaVms9JXzQRjRThkG1XKZQj5P4HlxXtZW8Yh+RM9MvlCAIODqpUs7mnjuFR7olI+v1PwAUCmBtmnGHc5zuRxmtxuSG6Qkq0S+9QTRYhBigx1y3aiFRbfbZXllJSZaGIbBxPj4tveUjUaDldu3ee7ZZ5MX3/qNA46JA2J3gzAgJUTdD4YgWVNr6DqZTCZkfWUy2x6DhLjLnjAMkJJSIljYj0q5jKci+inDoKqqtSCcrLqOE7YBVR6U7TiYpkm700FXnR3ic8v1yiFdFfw31ta4ffv2fd9+5IFdaX3fRybSBBC28rBtm3FVL7tWr9NWX/BEtTowMDTssdzqSxOKPRWRLyxVqdNSFL/tGN+nn37Ko489NvQhHYRhE82w1NOdYqcPRi6bje/DVojSag1F0IAwJlBUnfM2w8TEBLlsltW1tZA3Ho1X7f2Tms2ZhEpmEAQ0VNooophGLrIglL/JZ7OsLC3FY7pf8cAarXScHpE03/dpNBrkcjkMw2CtXidQmsGVASJp8f6wzwgGSclshijNMT05SbVSiWmSUToi2Sg6iVqtRr1e55FHHtnJxx46yfh3c6W9A+iaRjabxXGcHsOJEDXrarXbNFQPWkN1FaiOjfXocm2FyYkJMuk0SysrYS9cwslKBsHA+51Npxkrl8mkUnS73VCGdUCaJ5vJYKtswv3sJj+Q7nEQBEjH6Wn6tFav07VtyuVyuG/NZinkcpuKj0UBnUHtGrcDKSWddjtm2gghwr40rovV7dJVP5oqJE+rhtAAv/zkE5548skto71RFZFt2+E5FfGja1m4qppIBkHcjc/Q9XiP7RRa+M9IPMKA1IfHJMaVX2CsnF+vgTUMDFX0HlXwVCoVsrkc6VSKbDZLOpMhm06j9UXV+5HLZrG7XaxuN9aXclw3pH56XjjJKuPO9LnR+hbFCklomsb01BSLy8ssLi/HPOWoQIEBUfvIBU6n05idDq12m3QqRSGXC1dp1pUoa8vLjI2NUSqVtjWerxoPpNHKbjcUIFMromma1Ov1uLA8qRe86aoZrdSqYGCn+xhTNYcqFgq9RdipFCXVTiTiK8cGLETY8Mo02bN7d5h+UtKp7VaLpnqta9vY6j1CqF6u2SypdJpsOk0mk6Go3H1N07BtG6F41rqqZTX/4hO8C7fBhRPPwePnoPC9AxiPTIR6x0FAkOg4b9s2pmXh2HbYjiSaIGw73rNHPWUz6TTZfJ6y6qxXLJVIGQapVIpWux3ms6PYgKoRTqVSGKokrx/6DlZaCFfW6clJFpeWuHnrFruUSN9m5xBCkE6n0dX9spTYeaFQiHP46VQKq9tldWWFvIp/3G944Iw2CAKCRJTScRzqa2thw6tCgalIAWEbPNr+4u0NerubwPO8sDPeEO5tOIRQsT+byeB5Hmtra9Tqdc589hmZTIa//pu/oaNST1FbyWKxyMTkJJlsNnyvkk+B4UQLgLV6nVQq1UPg14IUdhcC5THmLShnCmT7mnVFsB2HTqdDuVJZZxlF3GyIJ59oNW22WizcukX7/HnapomuaeTyeYxUikI+z+TkJGNjY/G+fzMI1V5zq2KFJKLA39LyMiurq+RUymfT6xByy3PK+2m127RaLQqFQkxvLeRy1FdXGatWY2mi+wkPnNFKJQgO4T72tuqelslkyEWdAeRwBcQN50usBpHhyi1WXSklrVYLgSIXbDwgZlqtrK5SW12l2WxSLJXCxslBwMFDhyjk86GCBfSsEEKIeAWNxLw3c6OjHOxmZXLbQVKQTg0k1CCWMu7nYxgGIpcjlcmQLxaZnZsL6Ziahu95WN0ujXqdtUaDa1eu8Gmng+e6TIyPMz4xwcTEBNVqdcNEFzHUtG26yRF5IpPJUCqXY+ZbaRtVRz3qFqrWtm2a+L4fMrB0Hdntxsa8XZLMV4UH0mghXOluLy/j+z5Tk5Ms3b5NWrmkO3Jz+46NvtDNzmNaFp6qFupYFn4QsLq6Gv7UaqyurqIJQXV8nMnxcfbu3cuYEkR7/4MPeOLxxznQF4AKVFc61/NCDWXfjzulJxGJrkWcZU3V7LqeR4awaCDiNYdUCiAmVKwT+mPDSHCGIxfeMIywlFHtp/uDdbpSnojc3ej4CLOzszQajbAhWS6HbdusqQns7NmzrK2thQUYExNMjo9TVWmymF66idHGhJDEJFcpl8MAU6MRdxXcEuo6mhCUCgUsy4qlegrFIrlMBlOtwv1tRO81HiijDVTfFsdxWFN72MnJSTRVOtevObwVIjrgBsNNMo36jNfzvFg25srVq1y5epVGo8FYpcL4+Dh7du/m6aNH447sSVjdLou3bnHs2LENryWDVYGqFZXKwHy17/Q8L+7F4ylVRgjlaToqTWEnUi4t4eLkJDIIV9FWAbA7pAc1x4K4qD+Sg9U1DV3Vsuq6Hq/+wAbDSUJXn6Vr23HQaXZujtm5OUAJ6TWbrK6usri0xCdnzmCaJidPnuSxxx5jdmYGbQCHOqrJ3VA9JASTExO0Wi1WazXGVTR6M0TFGhEbLK/kfyy1wuZyOYTrhtuBbaiYfJV4oIxWqgeq1WziuS6VsTHy+Twt1dR4EBVx6LmiL36T45PnCoKAldVVLl2+zNLSEkIIds3N8cj8PGPVak+ifxguXbzI3n37Nne3EmmoWFdpCBlEJlZIIFaRjI5zpY7mCoIg3C5kHcgaGbJqGxF9OqFynI7jkO52GUu01ex33beLbCaDrfSbsn0PvKZpjI2NMTY2xsTEBCsrK6RTKWZnZ7l+/TqnTp2iWq0yNzfH7Ows+b4OhoOQMgzGKhVWazXWGo0tReJg/fsVAIp8o2taWHzQblMsleIJZiqh4nmv8UAZra/YTVFnu4guGClJ7HTvkWT1DILreSwtLrJw6xaLi4uk0mnGxsZ48YUXmJqaQghBo9HYtI1FPHbf59KlS7zxxhubHrdZZcqG8Se4yCnDINs3aWXQwYPAD49Lu6GEar8RRfDuIgsoEnCzVXfBQVhYWOD06dM8++yzfPTRRzzyyCPk83k832d5aYkbN27w6ZkzZNJpZufm2DU3t6mrWsjn6ZgmjWYzVArZjjhfX64+lUpRKhRotNu0223ypRKupvW0jLnXeGCM1nMc2kovONb1VauBq/SKd0KfG/qalKzWaly5fJmbCwtMjI8zt2sXTz75JFa3GwYvlEgcqKjnEAJFEteuXWN8YmJLdcWtJpKBY1aBsy+DevdFzpjN5Wi3WgMf+PPnz3Px4kVeffVVxsbG+ODkyfgYQ9eZnZ1lemaGQErqtRoLCwucOnUKz/eZ37+f+fn5jY3IhKBSqWB2OiytrLBn1y6MbbjJ/ftowzDIZ7Mha6teZ2puDtM0e6Rl7yUeCKOVUtK8fRtfrmsDJwn2juNsm3A/bCWzbZtr165x6fJlAObn53nrqafivUwkzlZRRe2RS7VV4CTChc8/55kBe9ltY5Nr+EFwx2oVg7BBII2dTyQQ9jXSVWeEyCCDIOCj06dpNJu8+cYbZFU1lOd5oTJjsoJHjaOqglVPPvUU9XqdK5cv89d//ddMTU0xPz/PzOxsXCShEVIdl2/fZnV1lZltuLWRt5Ist8yo9FGn1SKviDPDBA2+ajwQRttYW8NXhum4LlnFc4V1mc7CNlyXDXtCYPn2bS5fvszi4iJzc3M8++yzTE5M9Ox1fd/HUhKoPcn2KBWjghnDUk2Li4thsGQTFf3kOQelnDbLIUsp7wp9cTMe9nbZSj3vI6wAivrcBkHAiRMnSKVSvPbaa3H+2YnSeAOuoQmBF3kSQHVsjOqzz3L06FFu3LjBZ2fPcvr0afbPzzM7MxMzrkrFIs12m/wQwb3+cTLgM+ayWXzfZ3V5GUOVHw5rM/pV4r43WsdxcNrtmB6o6zrpaI8UBEjfD5URd0i6v3r1KmfOnMEwDObn53nm2LFYbLwfplJmyA/6woRAqgcqqa8kIWwMBXz++eccOnRoxyVvyfFu9s7A93dUdLDZdWBn3OutkM5kMLtdamtrfHT6NHNzcxx56qkwJRVFv11308j/oNxt9L3Nz8/TbDS4fOUKPzt+nHKlwtNHjzJWqdDtdqnVahQSW6lBSNZN9+fLi4UC9WaT1du3KZfLI6PdDppraxhShtSzINgg2Rnd4i3ZTyofeeP6dc589hn5XI5vvPAC49XqpsbkeR5d2yaXzQ50QaMHPFoJ44gsobpDq9lkrV7nV156aTsfd1ufJYkoqvpFiRXqZJtep8eYt8sTVvfgw1OnOPrUU8zPz4dpm8QxUQ+lYYiIF8O+p3KlwrFjxzjwyCNcuXqVd3/+c6rj4xw8eDDsMbxVNDlZ/N/3uYQQ5HM5Wqr16dg20klfNu5ro+12u/iqZ4ulkv49q6EQ602QN3loI2P9TNEHn3/uOaYmJwnYOp1hdjoIGKpEkWzi1c9aEoQBqP3794dudTRG9dAOHXG/a7yJgUQ0w7vlHg8Voev/+xB3FnqVMC5dusSZzz7j6NGjzA6RK3Vdd6AEbXwp2LL7AeqYffv38/gTT3Dl0iVOvv8+xVKJmbk5KpsIHgixLu8qVKeJJDLpNB3TpL62xvT0dK9e9j3AfWu0Ukqa9TppVK6w3z1VD0ag/j3oYZNScvPmTT49c4Z0KsWxZ55hempq2yuZ6zjYnrepezWsxC+6/pWrV/nmq6/2jk+503eyT+xHpFjxZRotDNjXRqtlgpySfF36Pr/85BMWFxf51re+ha8KEgalfzzPw9giJiHUBC03mZwjj8PQdQ4dPsz8gQNcOH+ez86eZXl5meeffZZyQjO57834QTD02aiUSqw0Gqyuro6MdhhM00Q6DjnV5jGqIImRTIyz8aFtNBqc/PBDBPD00aPMzMzsOH3RMU00GJpnDIexHhDrXytur6yQy2QoD0kVDJtoYH1PnCTsD5qcYsWKuxE9HjLxxP+GeLKJBN8GTViu6/LBBx8Q+D5vvvEGKaXyEfF7+ytnkn2BhkFA2G9pMxc+CBCJcxu6zhNPPMHU5CSfX7rET3/6U+bn5zly5MiGVTfp+QwSVjcMA11KlpeWmJubu6c52/vWaLumSVp1BgikpJB0TxOze+zWROH6IODcuXN8fvEiR558kv3799/Rfs+2bVzV9Hkz1zvSZPKDgP6v8erVq+zdt29H1+1ZuSM6ZbQCqEBXsiLJD4JQEjTpescrX3ig9NfVFXuYRUmDS6ykPRNHcnDJvegQ78Y0Td59913Gx8c5duxYPJmm02k00wx79/QZrWma5O5CJ7tASlIDxjQ2Ps4e22bP3r3cXlrib/72b3nuueeYVumgSBI2iX7PQgLFYpFGs3nP+cj3pdFKGSoplg0D27ZjUrp6sWfPFwUohKaxVqvx4alT5HI5vv3mmzH9bRiGmqKUsc7uVpzT6KHs3xv7nsfNmzd56siRLT/vpugPjPT9jgJEsQEl6YkqMiZ0kXjTkGDSAJqg6Pv3VsUYtVqN9957j0cffZSDBw/2HKtpGqlUCkcF9ZLomCblbRScCxEKjQ+KQ0SFBIO2CYauUyqXqTcaPPHkk7QaDU5+8EEYyT5yZD3ekPj8/blpKSWZdDrkeXc699Ro70u5GcdxEL6PUKVpWxUCSCk5f/48Pzt+nMOHDvHyyy/HBnsnMdWu4+ArCc+tEBlM0MeKWrh1i0lVF7tT7GTMgSpnuysYUDyRRNII+6fCG9ev8+677/Lss89y6NChgcYdlSG6fS08LNPc1r2G3gj9hrGHgxz4vlKxSErXqa2tMT0zw3e+8x28IOCv3n6bxcXFgZN78jNEKT0daN7jViL35Upr2zY6xHumOGI84KFaWVnhww8+oFKp8PLLLzOeKPPaCsMez65lYej6tllWUUvLJK5cvcr+/fu39f5+yMSsv9Xn6Cdi9B4vkTJRzRSov9HrYq8fvfmE0XNfE4SSs599xtVr1/jmN7+5KdUvlWiklUrsKTs7dI8HRXgHtmdJICpSuL26SrPVYqxc5pljx7i9axenTp1ieno67KPUZ6g9d1+EogbNev2ecpHvy5XWNk0yuo7jumFXtCErycrKCh999BEVpTDwwQcf8Ndvv83p06dZuHUrrAXdIVzXxfX9HSXR+0XJrG6X2uoqc3fYkS2iSMpI2Z/1QFRyXxoEQdj5HdXiU+1v45+k96tOHNuc+ntUS9vThydBEkFR/DasYCJUPvzggw9YWl7mjTfe2JKbK4QgncmEfZES4zJNc2NT6M0wKGCWuMYw5PN5Muk0jUYDW3lGU1NT/Op3vkO32+X48eMbGnn156YzqhuCleiI8FXjvlxpPc8jrQIwqch4+lbZ61ev8vEvfsGzzz2H63lMTkxQLpVoNpssLS1x8fPPOfnBB1SrVaZnZpiZmWGsUtm4kvTtZbrdLgJ2VD+paxp24hzXr19n9+7d22dpJVYtZNgKM2l88ao7YOyBlKTUnuxOtgLJ8rRoT5gMRPUbSDgZSCzL4sR775EvFHjttddiLemt2FRpFUl2FS3VUxTGnaxaQgg06InwRtuTTYX8CGmQC4uLtJvNuNWLbhi89Cu/wi9+8Qv+7p13ePWVVwa76yKspvJUne3Q9NGXjPvSaHXAcV10ITaG5qXk3LlzXL50iddef51CocCNGzdixYZKpUK5XObw4cN4nsfy7dssLS3x/vvv43keMzMzzExPMz0zQybRkAtCjnFXNeHaCZUvetADlSe8cuUKzzzzzIbj4oc6Wj2TD3lilRPR65sQGKLzbZZb3Sm2jAGo8TQbDX52/Dj79+/niccf7408R4HBBFMsGWlOKfXHrjLazk5X2cRYkluDSBtqK1kewzBCbSjVMDz24jSNp595hs8vXOCdv/s7Xn75ZapjYxtcZN0wQi76aKXthQgCXNcl05dukb7P6dOnqdfrvJGoEBEwUGvXMAzmZmeZm5tDSEmr02FpaYnr169z+vRpSuUyU1NTzExPU61W6do2Qsrt1WEmoCt9qcD3aXY6eJ7HhIouRqtnZFw9cq3DjK3fkIcgOtfdCkRttVIKYPHWLU6ePMnRo0fZs3fvgIM2Ei3om1zS6TQdy4pFy7cbhOofS9Ir8H0fjcH3NJogI6ZWqVikVqthdbsU+q596PBhCoUCx48f57nnnmPX3FzP96apCHYnIZT+VeO+NFrf85BB0KP3I4GTJ0/iuC6vfetbPSuwpuv4Snx6EHc0en+xUKB04ACHDhzAU7pOi4uLnDp9GsuyKJfLMU0tuwOygqbrSCHwg4BbCwvhXjZpoDt0XaOc81ZGe1dbgZCgHw557eLFi3x29iwvvfwy1W0oQ8ToM2QjlQLbDhuWmea2m5X1QxMCP2m0A7YjElTjsXXkVKe/Zqu1wWgB5nbtIpfN8u577yGEiOmXkQekaxpWp3NHY74buO+MNlCaSEK5xpEu0Llz52h3Orz2+usbGDWGrm8tnSnWu8sJwNA0ZqammJ6a4siRI6zV61y7fp1arcaFCxfI5/OhGz07y8T4+Ma+sfTlLqXE830WFhY48kVzs0nXchPExJK74B7HFT6DrhMEfPzxx9RqNd58802y2ewXUuA3DCPeArWUSmV48e15GBvGrgg46cRzEU1Ag8apaRrFUolWq4XjOGEqqu+aY+PjvPTSS7z77ru8/vrrFIvFeLui6XqPFtdXjfvOaFER0WiVFUJw48YNLl28yJtvvjlQPFrXdbq2vTWhvH+fReIhlZL9e/ZQGRtDSkmtVmNxcZFPfvlL2u02U1NTTE9PMzMzs65ZFAVxlFq/2enQbrW+UDf3nUDexZV2WPTVdV1OnDiBpmm8/vrrGIax5QS5HaQzGSzLYq1eZ/fu3WoQvVuH7aTtNE2LI77RsxHFFzYz/lKxSLPVotlqMTkktVcdH+foU0/x7vHjvPHmm6QymXiidFUP3HtRFH/fGW3gOOgqKiqB+toaH330Ea+++mq8h+2HplphbBdRcCGaOV3XxQuCWDNXCMGE0uh98siRsC/q4iJLy8ucOXOGdDrNzPQ0M7OzTExOous6hmFw8+ZNppSS4BfFdh7YuAv93XhwBqzanXabn7/7LtMzMxw9ejRUL9zm2LZCyjDoAo16ndKAKGwPlXKzgJyU+MpoNU3rTV1tAl3XyWWzdCyL6iYElb3799NotXjvxAleffXV9TSiem6+SIvSO8V9Z7Se46Cr1hFmu83xn/+cY8eObar0HreuDIItQ/4Rkqtut9tFgw1fQPSAptJp9u7bF/KIpaRer7O0tMS5s2epNxpMTEwwNjbGzYUFDh04cIeffMMAtxWIipg6XxT9BfArKyuceP99nnjiiR6N5iiH/EWRMoxQYzmV2lSrOHm9QeSPqKwu2vrsZGylYhHr9m3a7fam6Zunjhzhvffe4/RHH/HYY4+hQexZjYwWQnUKJX598tQp5vfvZ8+ePZu+xzAMJGC77qYVOYMgpYwlbECtXpsZgRBhu4hqlccefxzPcVheWeHG9evU19b49MwZamtrzMzMMDU1dcesmf4RJAkV0e+ol1DHNHvSSNGD2xYudlZ1ggfaOYlwTNxWK07LRIUIvu/TVTzv69evc/bsWZ5/7jmmBxBE7lR+pu8kdG17Rw24e/jWitAiCPP6dzJ5ZVUX+NYWRosQfOMb3+An77zDjZs3mZycRBAWtbCTgNxdwn1ltEEQ4LsuhmFQX1uj1WrxyiuvbPm+TDqNECJuarwT2KplZjqVuqMVxEin4+ZPq7Uazzz7LGu1GpcuXeLkyZNUx8aYnplhdmaGcqUy9MFKMpx838dWLSODhKH2w7IsJIqrDRsMUQCaBKm2oFoAAhGvSIFq+SEJ92iObfPZtWusrKxw7JlnSGez1Ov18L2qqZemouSa2sdHXtGdoNNuUygWB5brbYXk2AMp77hRVqFQYK1eD1lZm6SejFSKp596ig8//JDZmZlwkrtHfWzvK6MF4i/wwuefc+CRR7alAphKp8OEfaIx13YQucZCiLjSo5+Lu10sLS0xNTVFIZdj6tFHefTRR/E8jxVF7jhx4kRM7picmmJ8YgJd7cWjn+SkEdIOBZqmYShlf5EwnMhoNNUpb+DnkykMW4S6x0DeFhTTObIDjjctizNnzoQ1sG++SUp1bQhUZFaqzgZBEGA7Tg/3NwrE6bqOpusYqoXmViWRnXabUrWKq7S/NoUK/PVzjn3fJ/B9sqqn0k6n3WKhQL3RoN3pbJkvrlQqZLJZbi0sMD0zsy296y8D95XRStXqYvfCYy8AACAASURBVKVWQwYBM7OzdDsdilvRxaQkncnQ3SZLJUoHeJ6H4zhx3q7/C4/dscR1BrrOUrJ46xZPHDnSU8FiGEYcrDr82GO0FMXy8uXLnD59mnw+z8TEBNPT01THx0Oeta7H7Sr6C7EHfY7t7uE3g2VZ/Pz4cXL5PC++/PKmLr2UknzUosT38YKAQE06juP0eASa6o4QlVb2G2aj1WLPvn04jjOQ693DhR4SDfY8L6YXJqO52zXeSL3R6nY3rZiK2HJPPPEEH548yfjkJHIHwc+7ifvKaKMw+rnz5zl27BjFfJ52p7MtXeOMaha8mauVLPIWUuIq1ziTTm8a+InNdIBhA7RaLYIgoDo2hmVZOI6D57q4nhd2JlfnzWSzHDx4kMceewwB1Ot1lpeXOX/uHFa3G6eUpqemQsXJbRjtFxV0W1tb47333mPf/v3Mzc1tiy8t1EqvadqGByiQksDz8BINxaJGYlHuPSLGmJ0OY2NjdBMGk5wgeyqKhsB1XTTlKSW3ETsx3pwSJh82eUBY1ICUzE5PMzk5yfVr15hRvYm+atxXRuu5LktLS+Sy2VBkWgh028ZSPVyHrXIQ5v2ife0gDZ+YWJHg19q2HadrtpvKGOQ+37hxg4nJSTqqOXQgQx1iwzDIqf6ygzogTM/MMD0zw1NHj2KZJkvLyyzeusXHH39MNpsNKZYzM0xMTGxYUe8G7zjZlqNarWKpYoktscl90oRAS6XCB0vFF6KOgNGPZVk0W62wBYjr4rhuODErksN2P5HsS7skA2Qb1DmG3ScpyWazSKBjWQON1lETcC6TQVMSNn/3H/7DwEZqXwXuK6N1XZeVlRX2z88Tqb4X8nmazWYYZBqUp1VfSlqtll3b7jHaOA3Q9zD4QRBKnyT4yzsaq1pBHMdhYXGR2dlZDE0jm8mEfWRyuR2RHnL5PPPzoY6v7/usrq6ycOsWv/zkE9qtFtOqyGF2ZoZcQpHjTtxjKSXnL1zg0sWLvPLKK1SrVUzL2nYEdqcTRdwRUBlXEAQsLi5SGRsjCAK6loXrOBSLRdKpFEY6jb6Na/i+j0wUlQwcV4LptWGqiWiJuh52gLesDdFgKSWmacZlhRBGnYvFIssrKzu5DXcN95XR+r5PrVbjueefj/9mpFLhflXl9DbIYEZ8Vl0nlU73VF9EaZJBX7+TdI0VtkpluJ6H7Ti4th1zXlOGQbvZZP7FF8nlcqyurcXnggF0x21ACMHE5CTVapUnn3wSx7ZZWl5maWmJzz77jJRhhBzpYnHHxQ0BPqdOnaLRaPDGG2/Ek9bd2h9vhqTrWl9bY9fu3VQqlbCmVhUQmJYFlhUbUiqTGWrAruqdm3wmhn2Hg3jVyWNzuRyNZhPX83oK9K1uFz8IKORyPTpcY2Nj3F5a+iK3445xXxltbXWVdDrdI5UqZVh147ku7VaLUrm8vmft+3Iy6TTtVmvo6ppE0jXeDFJKbMeh2+3G5X8pwyCnVo52q0VadaGH0IhdxZ2GPndaGW7kpkedCYYi8iIyGfbu3cvevXtDckejwcLCQtwlYXJiItwLz8yELTCGPeQGvH/jLNlqKaYk9o9tuxikWNiPYWQHKSUrq6scffppIFS79H2fUqmEVB6Q67pY3S5Wt0s6lSKdTm8IkEVR5+Rks+nEG03iURvPxHG5bJZGo4FlWaRUdL1r23S7XTLq+hECYHx8nAsXLmz6+b8s3FdGe2thgWqfYJYgjEIWVYF71Dd0kOuZyWRoNZtYlkVuk3xtv2scX0v01tZato2tOM2GrlMsFOKccITV1dWw94+CkUphO86GSGS/3lCUXkquPrExb+bSCcGY6ss7OzdHPpultrbG0uIiFy5cQAgRFv3PzpIr9wbvPj4KeypVjv7K8xsMdFD/oEGQ0U8icNcT4NvGOVqtFpqux/ffULlez/NIp1LkFMUwyldHza41XSebTpNKp2NSRb9YQfQdbqbfjHo9SKy+6XQa3TDCaq9SCcdxME0zjEuo7EL0eQMpKZfLWKZJp9P5ynWQ7yujXVxY4Nmnngr/E61U6ubquk5JVWZ02m2KxWI4YyZmy4hY0el0NjXayDXeQMSQEtu26ToOrir1y6TTZLPZHpcpiZWVFcYTRpsyjDidtB2KW78xJ400oG91Zt3djiKl/397bx4jx3mfCT91V3X1PdNzk8NLpCQekihRNEVZpLyykwWCNT5vjGyCIAly2DE2MZD8k80BJDASeL84RvItEmCD/BE4h77dNfKtvA6+lXzpsCySknhTonhTnCHn6jm6u7rrrto/3vetqe6p7umhKGmG6gcgOOR0V1dV1+99f+fzSLS5Y2RkBAhD1Go1Ula6dg3z/DzSewCZjn6O11U8fHD/CtcdQDTAj9g5xM+H/e17XnTf241BroYVCx29Z77nAbHdVBCESGfWcV3Ytk1ib9MkHVEtrjFDkvZPK1gdPH6NmqKgYZqwbRt10wTP89CpAHccTDupv78fN27cwB72zH5EWFdGWzWMxEYBdstEUUQ6nUbdMKJumogsHIRVQFYU1Ot19HeguHQ9jzQnxEpDDv2iXDpMndI0qKq6akmlXC7jgQceiP4tiSJ4oGuj7QQeQBB3s2Pufkg7gqLdnCZVMpkM0pkMtm3bBt/3cfb4SdycmkQYBLg+FKB+8m0MDw2hNDgIRZaXjTIIAFrrZGC7KpuGCnF3ia9WzJfLKxQERZ4nGdqE13McB0WWocgyPJpXqNVqsB0nktOMD2mspc0yvihqqoqaYWBhYQEaVdtbwSwCcq94QUA2m8X8/PxaL/8DY10Ru8Vb8Jr+P/azJElIpVJwHAeGYURk5uym6roO1/NgduiOijPpOa6LpUoFVcpEkE2nifsZTzy0gWVZcByneaGh2Uy2U68FrdxMTPKENZ1ErinQ5NpFzfJo3qnfffddLJhVfO7f/hTAcTh69AiKfX24NTmJF198ES+//DLevXgR8wsLkSRG2PIHQHNDPhBl9u+2+3iuXF4xvihJUkRk1wmiKCKlaZBlGbqmwfM8VGs1mI3GcrdUNzt+vHED5BkTRJHE0bQnuslgY+cVeSXchyPkvRrW1U7bdJPiN6Ol8UFWFOghIRSvVipIZzLRrplKpbC4uAijjYvs0/5eSRRJttB1yVC0rpP4iEsenE7C/MICIa1u+eJESSKyJp1ivHB5HjdyNcPlpv8mI0w4Rqcaree6eJPKchw5ejRaoPR0GtvSaWzbtg2B72N+YQEzMzM4feoU6o0G+ksljI2MYGBwsKle2Ur+FmXk2SITT6h1aFIBSJMCSzo13TNRJOwfXch2si6oDBXVsiwLtuPApgPtbKi9bZ83u4bY7xuWBduySBVCkppzJrHXBUzRgbrgn3ijbQcOZHWL3yCZJoQMw0C1WoWeSkFWFIiiCJW6yKUEF9mmCQafij6lUiloMZFqoHv3ar5cRl+CULREp5Q8z4sMpmk+NGwzRtbyucwwkkSn2j0wjUYDb7zxBvr7+rCPynIkXQsvCCiVSiiVSnj44YcxMzuLumFganoa586dg5ZKYYiyWBb7+shD3CaGbToLlqGNGXL8u5ufn09k52eTXd0YrUO9GJES82mpFBRFgWlZsGjyUFEUSPT3rWjliW6YJhw64ZTNZqPjR6+P/dxK8fOJNtom1zABK7KdNAmRzeVQNwwY9TpU34emadBSKZiUuCtex7QcB/Pz83Ap8Vq7BohujbZcLidSy0iSFE3OiC1xYqdrTES73SIh2zs/P48Tx49j565d2LF9e3duIkDq1YqCYqGAHTt2IAwCLC4uYnpmhjR3GAZK/f0oxZg7Op9yS0Ir1pU0OzeXuNDxHAeB5xMzws2nStpP5ZbpIl4QCLeX5xEX1zRhO05HxcMgCGAYBjzfh6ooUFUVLh1RjGvmxhN2HlMpFIR7yoS5Fqwro+V5foW8BkPckOL1QZ7jkM5kYJom0bP1vChFb9Tr0FQVAXWlLdtGEIYoFgod0/TdfA2+76NaqSyXqOKGSUtEnXpZ2yJh921X64w/MBMTEzh37hwe378fQ2vsiW3lmuJ4HsW+PhT7+khzh2VhZm4OU1NTuPjuu5AkCYNDQ+gvldBPp5VWBf3+ZmdmoqH61sVRlCTYq0xquZ6HEGjWKY5BoMlK27Zh1OukXZLGwMByvoCRyoVBgHQqFUltKpKEWhDAa7PjezSJKVKVg49DYHrdGC3P89CzWcwvLCSLD8drgr7ftItwINleQRDQaDRgGAY4nodhGMhls6jV6wiCgBCS0V1lNay221YqFeiZDOHZjcWg9M2QZXn1uDYBnRgRm14HKoERhrjYpSxHO6zG6iirKjZt2kS4nGhzB2PuOLG0hD7a3DE4ONicwGlBrVoFOC46x6b7S3faEIAfhm27oNjwwWoutCLL4Hke9UYDdarWl9I0hEA0HMAI3uLXzUp7ruNAleWmsmIYhnBpLTnkyPz0UyMjHc/jw8C6MVoA2LR5M6amp7H74YdX/I6jCaIwDIGE+AogX5QgCLBoH215cRHgeeQzGWSzWQQhYcZvV3Nt/bxOnTXVSoV08LR5vyTLAH1YOtGpdHEibXfaIAjw1ltvod5o4NmjR+9K7IsdC2ivg0NfFJ1PPp9HPp/Hzp07YVsW5splTMeaO5gBtzJ33JmawuDgYNvjizSuDTwPfMJwfUB3SLlNrNoEughk6K7baDRQrtfJdBJVQ1Rp4jEOUZLAAXBoV1u8juv7PqmN0+RXrV5flVXlw8C6MtrNmzfj/z91irgmCS5XN3GmKAjQ02kyqD03h0qlgmI+D47jyCgeVl+lgebaJP1w8hf9U6lW2w6fA4g0iBzH6dpokzLFiV1RIOWmCxcuIJfJRLIcd4umiZg1It7cEcabOyhzRz6fx9DQEAYHBzE9PY1du3a1PRartQax0k28d5yNbrZzjVcekAdo7B+C0BFxAAqFQsewRaAlu9ZkIZuVFkURt6emsHnLlg903+8W68podV2HpCgol8sYalmRI7expWbWCha/8jyP4aEhVAyDZAcdJ2qT69pd5TiA1Udb3NZKtYqtMcKzJDDdmhUlrHYf191ZEZX7t9/GprExPLJv310ZWxwspu0UnyXd8dZP5TgO2Wy2SZalXC5jZmYGx48fh2EYuDUxAdd1MTAwsKL5hLH3e0EAhbUbYtnrsWw7Gnns6ro8D0a9ThpmeB4D/f2waB85gLaGK0kSHGrgzHA5jiOJRcoiMjc7i92PPdbVedxrrCujFQQB/UNDmJqaWmG0AdrvOgw+zQaGQQBd16HrerS6yrKMhaUlqIpCGvzpbGQ7MEP1WUzaYhjVanVVIWRJksigAS0vrYZuPInpqSm8ffIktm/fji1bt35ggwUABMHqw/RJbvoq7xFFEUNDQxgaGkKhUMDN999HX18fJiYniSxLJoOhoSEMDA4S3RyODLO3qh2GYRjRyih09rXTJ3ueB5vWboMggKaq0QKRFkXUadIyDMNEdQPm/jIuLJ7no/o+qwHPzs7i8zt2dL5nHxLWndFu3boV544fx+7duyMx6bib0i7W9HwfhmEAYQg9nY7iVj2VQr3RQCGfR0bXwfM8Go0GGnSoQKMJLIaouYGu8ozrNw6fPhSrlT5YndDp1mjb/D/HEW6kq1ev4vLly/jUpz5F+KLuUbmhtQaefHLJZ9dtom1qehpjo6PYsmULtm3diiAISHPH9DROnzoF07IwODCAPM3sty6IFqWyUeiwQOsCHoZhpGbn+T5CkAGSiHwg9tzoqRRMjoNNqwm6pjUtQJIkIQxDOLYNVdPIED91lyVRxOTt20jTuP7jwLoz2kKhgIGhIbz33nvYt3cvkriSWldaPwhgUFrQdCbTFA9n0mnU63UsVioQBQHZXA48x5FCfGz0S0ulIp4hxI6ftEjUarXlgYUO4HkekijCcZy7U4ajCIIAZ06fxvzCAo4++ywURcFSpXJvdllQo13lWrqtnycePwgwMz2NvbHGep7nSe23vx979uyBZVmYmZkhg//vvANd00gsTPmzHMuKGmrY+XAgHphjWbBtGx7dGVVVjaaxGKNlK1hZ0LIs1MOwqQTI8/zyFBC5yEgHmOM4nD93Dv/23/27Va/7w8K6M1oA2Pfoo3j9Rz/Ctm3byM1suek8lh+iEGSqBwDS6fSKBJaqqlBVFUuLi8jl8xGDYVrXyYprWWg0GrArFQg8D43W9NgulrSqV6vVRFb8JEiKAof2SHeSYQRinVIxuI6D4ydOgOM4HD1yBKIkRe7jvSrrh0GQmPhbfkEItOODXqVtESBNH7qud0z+qKqK8fFxjI6OYqlSgeO6mC+XceHCBdRqNWTzeYwOD2N4eBgpXSdEcnTyh9X4dbrwNi0ktD84yTtj52PRTio29cW6v6JnLCQz1YIo4tq1a8gXCtj+MbnGwDo1WlXTsH37dlw4fx5PHjy44nXx2896WXVdb/vgZbNZVKtVNOi4FQPHcVA1DYqiwHYcmI0GanRwQKFD7swdazXa1eJZBlkUUQcxPmGVkkzrYxXJcpRK2LNnz8rh7Y9qp02I6aNfYfUOrztTU8m19wSwkkxe0zBYKuGhBx/EXLmMxaUlLCwt4dKlSxAEAcViEYViEf2lEtK6Ho33IaFvPGy34IAYru/7sEwzYo5kQwRsAMH1PDIeCuDSlSt49siR7jPYHwLWldEytj7X87Bz1y5873vfQzlhIoS5LoyjiTHFt0NK0yCKYrQjM7ApGo7jSBubohDuJ9q/ajsODI6DIkkQJYkMX3McatVqsjZrAgRK6mavsTuqXC7jzRMn8NDDD2Pr1q1NWkXMSO5FTBvF7x9SZ08QBJicmMDTTz/d1et5ngePZZFoy7IQhCH6+vrQ39+P7du3o16vo7K0hMnJSbz7zjsoxpo7MplM087P9H06IZVKoWYYqNfryGQy0X1l77Np1vrypUvYPDaGfKHwsXRCMawrowVI8qBhGMhKEnbv3o1Tp0/jM3G1PHojfd+HSZkFujGGlKbBNE3U6nWkdb1tplYSRUiiiFQqFZG32bYN03EAw4BM48mHEhpA2l6TqqJuGKsy6bMzev/mTbxz4QIOPPkkSgMDAJoTYq00oR8EkfLeXb5/tZ22XC5DVdWONe0V4HmYpgnP81CpVhEEAWRFgUIpZwr5PMao0p7rOJgrl5uYO5g4WqlU6qqOynGEQNAwDDTq9abnyfd9eJ6HRr2OqakpPPfZz0K4S6mXe4V1abT1Wg2u52FsbAyzs7M4fuIEnjp0qOkhNU0T4Djout5VbCcrCin7LCwkCgm3guM4wk0kSdBTKcJZZNuwKf2n7ThYWlqCJMvE0DvUf2VJQh2IiNHbIgxx4cIF3LlzB58+cmTFnO5aSy7dIOo77lSj7bRTrRLTTkxMrOqVMIpV1/Pguy4ajQYs20YqlSLJyXy+7X1rx9xx/fp1vPnWW8jnctGgQy6bbXvPBEFAKpVCvV4njTkgC5pt26jX6zh9+jSefOIJwirZM9pmKIoCThDg+T4kQcBjjz6KN44dw+nTp7F//34AZDTL930ywdFN9pK6gJlsFoZhoFKtki+wS3C0l1iSJNRpdpJx9pqmiUYYRoTZSUbMmAUty2r78PmehxNvvgnbtnH06NGIrjMJ3bIydINu1OTv9vN838ft27fx3HPPrfjMuJH6QRDN5DJOJl4QSEKQ3u+uwHHIZLPIZLPYsWMHae6Yn8fk7dt488034XneMiF8QnOHREMZ13UBWrUwDAPnzp3D3t27MTA4CA7thxU+Kqwr5gpg2UAcyhzP8TwOHjyIhYUFXL58GQCJc0T6pXYD3/fhBwGy2SwUWSZMDXch6cABpD6raUilUsjmcigWCshmMlBVFRyIB1CtVrGwsIClpSUyXWRZ4AUBAa0ltsIyTbz62msQRRFPP/10osHGl6bWstQHQeQetxsB/AALxPTUFHK5HATarFBvNFCtVFCpVGA0GkQ4jBK8ZdNp5HM5pHWdzDeDuL6tRHpdg3ZODQ0O4tFHH8Vnn3sOz3z60ygWCpicmMBLL72EV155Be9dvIjFhQXiLcQWCM/z0Gg0cObcOWwaG8P4li2RR5FktN/85jfBcRy++c1vJp7OpUuXoCgKnnnmmbVfSwvW3U4LkIweiwF5mtF76qmn8Morr0CWJOTy+aiutto0TggqhUh3w2KxiKmZGSwsLqKUMNfZERxH2BFaWB3iRNyM9d7zPLIT084bgNR3bdtGJp2GIIoQeB5GrYY333wT27Ztw44HHmg/Pxt3Q1vGAOPnx6Gl5ZKWLlpr2+zfTfFxQrtlN9lhAMuKf1Tbx/N9XLl6Ff2lEmq1GjkWFRPTaNNDu3iT4wjpvCzLXU1krUDYzHfNkYNCT6exNZ3G1m3bEAQBFubnMT0zg1OnT8M0TQwMDGCITio5roubFy8irevRzDTrjEvSOmKJtuPHjyee0m//9m/D93389V//9dqvpwXr0mgVRUGNI4yGCh3X0jQNTz31FF595RXs27cPhS66UeIykSHIQ6MIAtKpFGq1GnKZTEc3NAnOKnKarUYMLLuDIZ0y8miNken47Nq1CwODg6gZBjhuWSeHeRoCVcxjaLvTxuu8LQtZkvGF9Nw4+jlJYLFdCNLLG9D3MDW9wPfheF5ENBdyHCG2830sLi7isf37oSpKdE3dgB2fucdrBseBi10/u/b4As/zPJkHpuU0yzSJLMvMDGbOnYPn+5BlGU8/9VTTgsZxHFIJSbX9+/dD0zScOHFixe++/e1v4/vf/z6++tWvYh/lev4gWJdGK4oieFmG57pkpWXtZ7qOfY88ggsXLsDzvGUWxJZpEKD5gQTQJHlRKBRgmibmymUyI7oGWLS1bS1gshi5bJZkKjUN169fx82bN3Ho0CGkMxki2OW6xCjYvHB8SILuohzHwXIc+J5H2Pjp9bMmEPZgxX9mMT2jjg1ju2/DNBH4fiQwxX7HDCcMw6j8wu5xdE9pg78kCOBlmTTT04b6G9euYXBoCOm74ARmDf13HTsmJezigyYJHoWqaRinImTH3ngDVcPA2ObN0U7Prlml5cNWSJKEAwcO4LXXXsOdO3dIYgyk8ed3f/d3MTAwgK997Wt3dz0tWJdGCwCKphExLfqgMDc3n8vh2WefxfHjx7G0tIT9jz9OOo1i7mOrwbKvkH1NAs8jm8thcXERNcMgrPxdwmI9x11O7sQh0VnNk6dOwTTNSJYjDEMEstzk5kc7WUwXNghD+J6HkJYhmvR44w9ly3kFNKnCGkfiLnSj0SDxHzUUZuhMFxccBzm++9MWv+jexow6jlsTE03Ust3CcZxlooI1xtPt+qBbebdaObfY81WrVvGTN95AqVRCX38/MrkcgiBocuP1DqWrw4cP47XXXsPx48fxhS98AQDwta99DZOTk/j7v//7uyIoSMK6NVpVVdEAIoa9MAiIDIQoQkulcOTIEZw8eRKvvvoqDh06RGhl0BynMSTFvJlMBvV6nbTYdeARaoVtWSgWi10V7VvhOA7OnDkDjudx+PBhyHFDbSmdsCYDtA4z0MWILWBN1xm/VrZrUoPlAOQymcigmeFxHAdZFKEnLVwJfd+tSIqFjVoNtVptxaTWagjDEKZlkZ5tWe6aFXPFuST8/wrCvJh3FgKYmprCqZMnsXvvXmiqiqVKBaqikAmteC97h6rD4cOHAQAnTpzAF77wBbz33nv4y7/8Sxw6dAi//Mu/vKZr6YR1lz1mUBQFoqLAYbsJt0yvyYGUUZ588kkMDw/jRz/6ERYXFyPWxnaJqfj6ygMoUNW2xaWlrs/LtKwoEdXNPsuoUauVCl5++WX09/dj7969K7PXXSwA0ee12VHYVFKkFM8EnWn5SaDJH4G6sOz8uHYNCN16Ei2vu3btGrZs3QpeEJbd6S6O5bguGaXTNAjc6lpBTYh7Gkm/a/0v5vIDuPTeezhz5gwOHTqEUn8//CCAQiVKvdj3JIgitA7u/lM0/mXJqN/6rd+C7/v4m7/5m3vSCMOwbo0WAFLpNDzqCjLCt9Z4YteuXXjkkUfw+k9+gitXriSXcto85JqqQk+lUKlUml3NDrAsi5QFuA5E1bFdLgxDTM/M4NXXXsODDz6IvXv3QhLFqNE9QpdfKotF7wXYTtaNrGQnxJM+nufh1sRERN4W7ezsT5v7xpJ0PM9HvMPhWnbaTteQtMBxHCzTxPFjx3D7zh0cPXIE2VwONuWO4nkeCt1pGTq5xgDJlTz00EN4++238fzzz+OHP/whvvzlL+Oxezwsv+6NlmcDyQmyhgwjIyM4cuQI7kxP4+Uf/QjlVt3QDvFngU7+zMzNdeWORUYLJB6TuaPMYG/cuIG3334bBw8exObNmwGQZEYYhk38ut3WQxO5hu8SURa6Xea4y3OKx4gTt26hVColzxrH7xfXrBjIFjF2b9ccfqzhtUEY4vLly/jBD36ATC6HI0eOQNU0NBoN8BwHURCijriQ5hMAIN1FQ87TTz+NRqOBL3/5y+jv78ef/umfdn8NXWJdGy3HcVB1ndQ9WxgYW6Gn03j68GHsevBBnDhxAidPnYqY+zqBCSn5rou5VXRZAlqHjMc4jBExjGVbAQBhiHPnzuHq1as4cuRIk3aNLEngeD7Kkq4FUenmXrQwrtIN1a0ZxM/k6rVr2L5tW3fvidWVTSo9ymqgHJc8sbPyJDu4xQmYn5/Hj374Q0zPzODo0aPY/dBDEZeXR3mzA/odxxtOOI7rymhZXGsYBr7+9a8nErN/UKzbRBSDls3CqlZXN0D6xY2NjWFwcBAX3nkH3/ve97B37170l0qdP0NVkc1mUaEcue2yyXENl+hjsdJl9TwPb775JsIgwNGYLEfrZxp0rFCgsV9Xj16bJoi7AXM/O7n53Z0SSeqU5+YAYIW41ipvJhlsEEaJeD10tU+PssWrnSfHwXEcnL9wATMzM9i7dy9GR0eXxcyoay6KImRZjjiP2PegcgAAIABJREFU40dVU6muuKm20rDgwIED+LVf+7VVX383WNc7LUCV4DWNlALarLwhmgnMJUnCY48+iqcOH8b1a9dw4vjxqNzRDvl8HqokYa5cbiueFQRB00wr21njj3yj0cArr7xCmkEOH040WID2WHPcXe229wr+Kjttt2B3/hrdZdeSdHFcN+IYFujuxne5MLVKnSYhCEPcvHED3//BD8DzPD773HMYixksQFpPgzCM2EUiCc1Yt1hxlYWf4Rvf+AZ4nr/nyac41r3RAoCWy5FeVGpMK25Gi+EwFAsFPHP0KIaHh3H61Cm8/vrrmC2XE1dwHkBffz84ADOzs4kLBFOqCyj/bQT6oC0sLODVV1/Fli1b8Nhjj3X80jiOyDcy8rE1uaJtrnetCCmhW+J5rsHl5ACYjQZm5+aiuL0bBEGARqMBLj4UwGJ2nm9KcCWhU6LK831cvXoVL770Em7evImnDh3CI488smK3ZKLViqJAEATSitmiLiArCrJddOA9//zz+O53v4uvfOUrOHDgwKqvv1use/cYAGRNg6goMKpV8qCJYhMbQaeECc/zGB8fR19fH2q1Gk6dPAlZlrFr1y4Mj4w0rVqyKKJYKGB+YQGLS0voi8UjIaigMpC4A0xMTuLMmTN4/PHHu2ZpUBUFtm3DiUlvdoWWJM7dwg/DtoyUa81QX79+HZs2beqa3hSgA+5B0KwD2wqOW6lbxNpSE15uOw6uXbuGa9evo1gs4skDB1AoFAizYku91vf9yC3WYtQzPMdBU5Qo7CmWSm3P79atW3j++edx7do1/MM//AN2796NP//zP+/6HtwNNoTRAkC6UIBRqaBaq6FQKIBrowbXCg7EcAVqvOPj45iamsKlS5dw4cIF7Ny5E5s3b474mzLpNCzLQqVSgUZH8EKaaArDcCXPUxji3YsXMXHrFo488wzSaxj2FukoGKM6WZM7dS8SUVTycwU61LqT4Ps+br7/Pp759Ke7fo/neUTdTpYTDT3e7L/iu+Z5cC27bMM0cfnKFUy8/z6GRkbwzKc/Hc0js+641o4zo14HG4BnJAOMpYLJusiShEKHGP3FF1/E7//+7yOfz+Pzn/88/uqv/mpVls4Pig1jtHouB1lViRYpnQDpNnnD8TxC+qXxPI+RkREMDw+jPD+PK5cu4Z2LF/HAjh0Y37wZqqKgWCzCcRzMzM5ibHSUtLFxVLc2Ziy+7+Pk229HLYmKqnbVRRQHUx9nLlpXuAfucdQpdQ8Y8m/cuIFiX1/X7BRhGBKDoUR6iaAJv0g2M+5VxRojlpaWcPXaNUxNTWF882Z85t/8mxXHDBMy0Q3TJOJb6XRTTG9RmUyO4+D4PoZHRzvG/F/60pfwpS99qavrvlfYMEbLcRz0QgHVuTmyM1HWvW4K8ALtl/Up0zw7HqPwrFQquHLlCl66eBF9fX3YtHkzioUCyuUy7kxPY3RkJHKtWBnAtiwcO34ceiqFp+OyHByXyKrYDjJttDcta01jaB+0waJjY0U3GVkK3/dx6fJlHDp0qOvPtiwrIpRv511EAxAxMJe4WqthYnISE5OTCHwf41u24Kc+97n2IUbLM2JZFlwqyBXf5T3Pg09lLz3fB89xGFyjAuFHgQ1jtACg6DrkSgUeZc/T6Je+misXTb0guak8l8vhiSeegOd5mJ6exq2JCbx98iRK/f3kweJ5jAwNIQgC8IKAaqWCY8eOYfP4OB568MEVrmo35xSHpmlwKhXSZ93lZMsHzUxGUiBJO+0azv3GjRso5PMr+qDbwaP6rxJlAlkVNPlnWhYmJyYwMTkJs9HA8PAwnnj8ceQLhfZeB6uhY3kBcOmMc+usLuuQAsdBU1W4rotMLtdREvXjwoYyWk3TUFUU8L4Px3EIQ6Ikrbqz8TwffWntlNEBEmOOjo5ieHQUjm3jzp07uH79Oq7fuIGhwUGMjY7Cc138+PXXsW/fPmxqx33E6oxdtuHJsgye7bYfEZUJawtdwVixBvc+CAJcvnIFT3aZKQ3DEI16HRzQJPadBDYUcfP99zE5OYnFxUUMj4zg4YcfRqm/HxxPtIzbGWyI5fZK9ho/CFBvNCDwfDN5PL0HFm3wkGUZVq2G0cHBD61s80GwoYxWEARImga/XofAcYSNkU6ucGEYTfm0guM4gOqxxLtwWhFXM5BlGVu2bMGWLVtw584dTExO4uz587AtC0ODg/A8D3XDICtxUm/rGlxkANBSKRiUMG41w2UD3d0gGmKnySX2vqgbqnWnXYNrfPPmTeSzWRQKha48iwYlAGg3VRVQBfrZ2VnMzM5ifn4e/aUStm7dikOHDq1guhAEAX4QJLvR7DroeQVBgDqt1evxbDV9HoIggGXb0NNpWI4DPZe7Z6N09xobymgBIJfPo2zbkGjvbqPRQIoaDo/25R8esboe+8Jirw2p0SdhZGSEDLHncrh29SpGN23C3Ows3nn3XQg8j4FSCaWBAZRKpeUkCD2fbnctWZK63m0ZE4ZF+3WbZm7jNV/62cxgF5eWogfctCxSj6QTPxFDBsc1zc22QxgEuHTpEg4mkMknwaZc0gplxQTIvaksLWFubo78KZeRyWTQ39eHrVu3YueDD6K/WOx4Hq1lHGC5lh2/XwYVFtd1fbkCwBJc4TJBgEJ1fEqDg52ZMz9GbDijlWUZqq7DrtWgSBKZvxTFiAKmXUa5tQE9apOLf+EdDKyvrw+macJ2HAwMDGDL+DgQksHyudlZ3LlzB2fPnIGiKOgfGMBgqYRCsRgNua8GjuOQoq2NjuMsP9hBANfzoiRJ4Puo1moQJQkam0ChzR28IECiBhjVk2MZ2BRVnENIeKxYEsr3fYSeB4d+HjMRgbL9sxE/IVaWev/WLWQymWiX7XSNnu+jYZrgeB6ObWPqzh3Mzs1hbnYWqqah1N+P8fFxPPHEExFbhWmapPGiG48iIXZlCGimOqAqFCyODkE7i+h5G/U6QBeu4sAA8lTFbz1iwxktQGQ+5ijViiRJqNfrEOhIVzsIdBwuDvZgM1aITuA4DsPDwwh8HzPT0xgZGYGiKMhkMshkMti2fTsQhliqVjE3O4ubN2/izNmz8H0f6UwGuWwW+Xwe2WwWuVwusTYpKwp4y0K1VoOmaYRi1POiRUjgeQiiGKmYZ1losMrDxdzF+M7hOA5EUUQ61mft053a97xI2pFp5tCbAJEyWly8eBFPPvlk8ueFIRqNBqrVKiqVCubKZdQMA6ZpIq3r6CsWMToygkcefbQt31a3anxspwxiP0fHCALUDGOFwQLNsbzn+zAaDaLvlMshk82uSQ3io8aGNFpRFJFKp9Go1ZBJpRDUaqjWashls6QUxNzC2HsEUURIXUJBEPB//+f/jAsXLuCrX/0qHnv88abj/+3f/i1e//GP8TM/8zP4uf/wH5o+V6DKelMzMxgdHm5eKDgO+VwO+VwuolqxbRu1ahWLlQoWFhZw88YNVKrVyN1mhixJEgRBgO04UezHxMNYEwZ7iF3XhURJz+6m9MNi99Z4lpHJtWoiRbu968L1PFy7cYPUMnke8wsLcB0nMtBqrUZI3EUR2WwWqVQKxWIRu3btQiGf76gJ3PSZaxyKSDJYo16H53krDDa+GIQg2kw8zyOTzSJXLCK7Bk7sjwMb0mgBQhdjmiYargtd11EzDNSoml20i8W+RMZ44XseBEHAz//8z+OP/uiP8N//x//Ao489FmWV//mf/xmv//jHOPrss00Gy6DIMrK5HAzDwO2pKQwPDnasryqKAoWy/jFWQ7YTLSwsYGFxEdeuX0e1WoUdU6uX6U6qaRo0TYOqqtHPnusSlvs1JI3iYEQB7ZoGgjCEbduwTBOmZcE0zejnRr2Ombk5SKKIV15+GZKiRDIq+Xweo6OjyOVykGmLZqPRiBafrsAaIbpsIIknndidCAMiLu77PlKp1AqDjVPMBjSjLEkS+gYGoOt613zaHxc2rNHyPI9isYj5uTmS7UunYdRqMAwDmUwmGncDyBfLaEg9z4OsKNg8Po7Dhw/jlVdfxU9+8hM88+lP44X/9b/w4v/+3zj4qU/hV3/1VxM/l3ViDZRKmJ2bw9T0NIYGB7t7KGkZyKPuZ0rXoaVS2Lp1azRLyly6eUqg7QcBLNNEpVqFRRXMjXqdJJFYzEmpZQRRJDzRNLkk0J9ZXHvs2DEEYQjXcWBTMnjGVxxQhhCPllFkWSbGlkoR8e1UCn3FImzbxsjICPY/+ihkRUEQBERx0DSjxcAPAjjUY+hWaykCzfAHVGu2E+IxLOua8j2PGGwYIpVON7WdNtXPWSxrGPB8HwMjIySMWacZ4zg2rNEC5MHKF4tYKJcRWhbS6TRqhgHDMEh7miA0TYqIothEH/KzX/wi3jh2DP/yL/8Cy7LwL9/+Nvbu24ff/M3fbBtPSZIEx3WRy+cxNDiImdlZTE1PY3BwcFXhaM/zIpeN4zhiFNTNDKh6OScIyOVy0WA209SNY3FpCZIkRTKNAU1SeZQo3I/9CXwfrufhxo0bGNu0CQLPEwof10Uul4uoXXgaL0d8ywnXX6vVcP78eTz32c9GPFmCIEBVFMhUN9ey7WhhkUQRmbsghAe6iGkTfu/7PlnQwhA6nX9lpa1ojK/FO6nWauB4HqNjY6SnfZ0mn+LY0EYLkIaLbD6PyuwseNdFWtdhUNnCVCq1TC4GYrSO4yCgygWFfB4//VM/he9+97v4h299Cw/s3Inf+Z3fgSxJbRNTCuVjBsis79DgIGZnZjAzM4MS1UpthU+zpywRlqKauJ1ithQT/aLJmzjYgyUKAkSeR7jKZE3AcXjrrbcwSrl4G6YJx7aR72LcLI5z58/jgZ072+6coihCFwQytUTVB2uGAY0qs68lRmV94u1+12pcrG4eUIOVJCmad+YFYXnuOfa91ut1NCwLO3buRF9fX1cKe+sBG2KedjVkMhlo+Tws2yZuJ33gWY8r42xiEy2+70cxUJwS8zd+4zeiGmm89TEOkc7AMgiiiIHBQYiiiNnZWRgtw/amZWFxaYlwSykKGbZX1VVXdEEQoKoqHNtu8g5WgGuvDtAObNFaC6anp1GtVrFj+/YVv4tiSVoC48IQff39KBQKkEQRJs2IJ5LuJd0HNszQ5rpa32FbFiE54DhkMpkoho0PRLSWpUIAs1SG84GdO9c2Gvkx474wWgAoFouQUymYtIiuqips2yZGxEoClBnBo67osWPH8PzzzyNHd5yXXnwxOl67udmUpsGk9CgMgihikKqwzc3NRZqq1VoN9XodInV5NU3r2HbXCk1VwfN8RMfSFmtMRvkJ8WKnI/hBgHPnz2Pfvn0Qksbo6Oc3Gg14nodUKgWZ1nUz6XTkKdQMY7ns1hJbxhF1ayXc/3gSKQzDaLeURJHkMuj5sQF/BAGZx40fPwwxPT0N23Hw0O7dH/oo3b3GfWO0HMehb3g4UiYI6I7r+T5qtdpyry0t8J85fRp/+1//K8bGxvD1r38dIyMjeOWVV3Bnamr5mMAKTqhcLodqtbri83lBwBDNJM/NzWFichKObUeCyivmcNHcuZPIY8zz0TXYrRxZd5E1ZmhlzY/OpQ1uXL8OVVUx3GbiJeQ44v47DjRVXZF9lSWJlLXormvU6x1dZbYjC7FdMjrPWENItVaD47pQVTUasYuO2qbH3KcaQ9VaDaNjY6S+vsFw3xgtQL7kPG0/YzQiqVQKQRCgVqvB9zzIqorrN27g//kv/wW5QgG/93u/h2wmg3//sz8L3/fx3//bf1txXB7LD0smk0k0WgAAx6HY14cwCLC0uAjTtjuKdbH3dGIUjEb3Go1lChyuhfRsDbFiZBBdutSWZeHie+9h3969bV16ltVWFKVtvMtzHNLpNDRVhee6MGq1ttfs092RjyePYnBcF7VaLRrvY8MHcYK9pGENx/NQrdVQqdWgZzLYd4/5iD8q3FdGCwCSqiJdKCBNic4t0yQJKZ5HzTAwOTGBf/zHf0Q+l8Pv/6f/hEwmgyAM8eSTT2Lrtm04efIk3rt0acVxORDDTafThAgsIT5j5YZcLoeBoSFYloXbd+7A6RCTsuO2MzyOI2r3QRhGglutCRX6wq7uTxKZW7s9OwxDnD5zBlu2bIlCiFbYtk3cU0latVeXA0kc6roOjzY/JBmu7/tRDzQTm2YwLQt1OkCfyWQiVfaALXw0V9G6y7JQybYsiKKIfY880tQNtpFw3xktACiZDLRYLMWK54uLi/i7v/s7iIKA3/jSlzAwMBA9vL7v44tf/CKCMMT/+/zzicflQHbztK6jSjVXGVh9FWGIbDaLvkKBSEx4Hu7cuYP6KnFpp8SUKIpI0aQUaylsfdS73WuTlBravXdychJGrUZmhhPg0oENURDI3HGHz42uLwyhyDJ06vYb9fqK1/qeFyXKuNj/1QwDlmURd5vW4qPuLm5Zm6hpWIDFvaYJkefhBgE2bdmC0XZjlRsAG77k0w5yJoOQdj81Gg2YloX+vj784R/+IWzHgUVLMHFG+9179uCf/umfANDMY0IGmQOZNDJqtaaSSZ02pWez2WghSGkaxMFBzJfLmJmdRS6bRbFDLbDT8LyqaXBcF3XDIAMBrcdImFxKgkd3sdVgWhbOnj2LQ089lZh8chwHRr0OnuOQSqU6GyxW7nyKLCMMgqj8FNcJ9nw/GhwIwxCWZcGy7WinVmU52k1bryXE8mSVbdswLQsICT3qUrWKQqGABx96aNXrX8+4L3dagGrC5nLgaVN8Op1GEIbwaO9xGBAl8DjH8YoJESY3ieadLZfNolarkVgXpOTg0vi5NSsrSxLRaU2lUKlWMTUzk1j6iHf2JBkec5MBRCN5Sa9ZDQEdx+uEMAxx6vRpjG/ZksiQb9s2GdIQBMIL1cXAQhJUVYUkSVGvNTguco0FnofruqhWqzCp+53OZomxozmLHP/0kA481AwDDdOEIIrIUY0eUZax8+GH132b4mq4b40WIKUYJZsFOKLLkstmyRcWhpBkGa7vo1KpoF6vrzSC+CrOZlZjtd1qtRolhEzLgkDZ6ZPAcxz6+vpQzOdh0zi3E0k512YQgFF9MgHqu4Efzxy3MbZbExNoGEaiW2xZFoxGA4IoRtSnbYkHuoCeSi1TvYREWd4Lgqirir1GT6Wa+Kz4hM+NpototUBPp5GlOQjTcbBpyxb09fV1dV7rGfe10QKkGULJ5UhCg+OI7EcmA1VVwYPsGowy1YmP7sVqgeSfy//OZjKYX1hAQF23kPYRr8jqtiCTyRDNVo7D1PQ0FhYX2w/tt9lxVU2DSF3+TooL8T+ggwps0YmaFhKO3zBNnDt3Dk8cOLDCLTZNEw3ThCSKSFN+rnYG2y1HlkCJyj06M1w3TRi1Gjzfj0Yfo8UwvpDGJ3XogMMS3ZVlSUIul4Mqy6g3GjBME+PbtkWSHRsd921MG4coy1CyWdiVCjiOg0hdJp/utD59YDzPg+q6RB+VJUISdgw9nYYgCKgsLUVGwFZ+Nly/gmCbQpZlDA8OYn5hAUuVCox6HaW+PpJ5bX3QE2QvGE+vvbSEhmkS/RssLy6JpkJ/57kuEIaRe9w6NB4COHXqFLZt27aixbHeaBDmCUmCRnfHdp/X7dB/GIYIOQ6KosAwDCzMz8N2XYjUK4rXaeNhR3wBtW2bhAt00IBN6XD0nGuNBjaNj2P79u0fWP5kveATYbQAICkKuFwO5tJSlGnMFwokzvU80pds26hWq7Do8EFrzTHOwTs8NITbd+5gaHAQmq5HbXLRqFgHnRme51Hq74dpmlhYWsLUzAx0XUchl2va3eJTSvFzECihHWPDV7qcovFamhZal5TLly/DtW08+OCD0bUyMjbbdaHIctvuIQ5tFoz4uSM2Rkf/eLTd1LFtuHQCK63rUWa4ydBajdWyyP0QRSjxhRakO6tar2Ns82Zs37HjvjFY4BPgHschKgq0XC7KLgo8j3Q6HY2P5fJ50rfsOJifn8fCwkKTWl88xh0eHsbM9DTC2M4FxGqojEwNy25p6w6kaRqGh4aQTadRr9cxOTm5opTEmCnY7s14oGTKzN8wTbgtdeB20STjfU7yAGZmZ3H12jUcPHSI0MxQ4zIMA7brRmoL7dDJYEN6HQCiWVnHcVCt1VCjc6+6rkNRFEKZQ2eFmRsfJ6MzaShjmiYpv6XTUb8xGwyxLAuVWg3DY2PY8cADa5Iq2Qi4v66mC4iqChWIdlxVUUhJwbKQpYmqlKahVquh0Wig3mhAkWVk0mlo7KHlOJRKJdSqVbiel9gjGyFeMwTp041KFdSlztPFolwuo1wuwzAM9Pf3R40DIU3QMLDP0zUNtXoddcNANpOJapvtDMinHkVrqcSo1/HW22/jU08+GY0Xep4Ho9EgXUepVJS1ZWA7a+tCFHfTueZfACBaO5ZlkYQYz0NPpYi8JB1bFGj4Ej+e63nRTowwjMYSBUpswM4jBMnkLywtYWTzZjxwHxos8Ak0WoB0TXH5PMxqFQhDpHU9Wr11XYesKOhTFDLI3WigXq9jrlyGJIrQ02nC6CcI6C+VsDA/j36qttcObPdlO0G8psoeeUmW0T84CIPStkxOTERUNE3HiiV/OI5DRtdRpaOI6UxmOd6LyXKSjwojCce4wXq+j+PHj+PBnTsjXVnLtmGaJjl+JhM9+Iz5kee4iI7WpztnK/iWa7QoGyPLXjNjZUbHcRxc141YQDzPg0NbUdkiI8syFCqJGb8Gn3oalWoVluNgeNMmPLBz54Yv7bTDJ9JoAbLj6qIIs1JB4PtQVBWmaUJRlOghlWUZsiwjm82i0WjAMAwsLS2hUqkgpWkoFouYmZ3FrlhppFWvNg6u5W8ATVzNAsdFvErz8/MoLyxgsVJBNpNBLpMhpaAYZQ1Tpdc0jXT91OtIsc6kWMN8tBPRGDE+Snfq5Elks1ls376ddA81GnBcFyINHeLk7hwQ0dQ2ZXGZ0XIxTmlaE2eGxxaMNJ0AAsigAUC8D8d14dNzrFQqkW6SREtpkiQluvXsPpTLZSipFLbv2oWxsbH7codluH+vrAvwogi9rw8WnYG1LAuGYTR1NQEkccQaNBzbjgr3PM9jYX4ei4uLhClBkqKpoE7G23QOAKFXie1Wgiiiv7+fxG9LS2QqpVolTI6ZTHRurKQjSxJ8WYblOOApk0TT7hcrDbGBcAC4cuUKqrUajhw5As/3Ua/X4dOxRq1l5pclkFgNOSo3seuk18zYGx3HiYjEJUmCQrmkmuJb6vq6nofFxUXUGw1CEEDr0TJl1WjHYhHSmHupWkWhVMKWrVvXpkK/QfGJNloGNZ2GKMsIACwuLKBCDSRpEkaWZfT19SHv+1igI2HXb9zA4MAAREGATOlNRTqdEz10nU6A/Z7nEfp+tJuqqgqVDh7EjZeVeRAE4GiMqmkaPKq32o5OljXhA2So/fKVK/jM0aPwgwAN2siQSaebidBi54iWn0OQXdIPQ7iWBdt1o24viSb3JLqQsV01oEbKuJxZLGrZNlKqikI+v+yOx8675ULg+z7K8/PwwxAjtKSznmlP7yV6RkshyjJyQ0PgBAELc3OE2ZHuak0PDf1ZEAQUCwU88MADuPDOO3hg+3aSZLFtmI1GRNTGhKbiZN+JDQn0T0B33XgJpdV4K7Qs5QcBSn19gCAAQUAGGQwDRr2OdDrdpD0bAlESqlwu4+TJkzh48CBpEKGD+nHZx6RzZLEnx/OA58GmCTyWvRYEASlVhaQoUUzr+z5cShrnet6yWh9d4CRRJMTpoohsi4pdUt93CNLkUV5YgJ7JYPuWLRgZGbmvSjqroWe0MfA8j/zgICAIWJiejgjiWNNE6wgdS0YpioKaYWB0ZASO58G1bUKH6rpwaFN9xJYYI1ET6M+M3hVoZvhvbXxQFAWDQ0MwLQt3qCiVZVlIpVLIpNOkxhkjt8vQchYbxxMlCQsLCzhx4gQe378fAuVzYgRzTUPkcdCdzYs1oTAiOS4ModFMLkCM1DJNQjIXI1rneR6SKEJkCxg1siAMCblaGLbfKalrbloWFisVOI6DgZERbE1oAvkkoGe0Ccj394MTBJRv30a90UCaqsGzETBWOwXItMqWLVvw3sWLGB0dhSyKkCUJehjC8Tx4NBHj+/5yvzB9CAWeJxQ4QCS/weJApq0Djlvus6V/p1QVRZqxdulAeM0wSHthOg1d01A3TdQonSzjmDKqVRw/cQK7d++GmkpBFASkdB2SIDSVaFiW2PU8uNTlZSRpACJ6Vo56BbbjIIj1UjM5EYkas0hf3woOgEtLQHJM4yf6PTu+aWKxUoFtWZBkGXseewzDw8OfqN01jp7RtkGOatTMT03BME3olN+JZUaZq6goCoYHB3HlyhXMzs5icGCAHIDnCek4JfJmuxPbsdgAgu958AFw1LA8z4v6pKNyCBDt0Ewsy/c8SKKIfD6P0PdRN0006nWU5+fJhBNtNgiCgLjJYYg3jh3Dgw89RMjlaJbcdRzYNIEUUg5kl54rY41gOkEC5VhmiSjX88DR+Jn9ThDF9nXrMATYbk7vYa3RIHSuNPkX71s2TROLS0uw6Vje0MgI9jz66H2dGe4Gn+yrXwX5YhEcz2NhagqVapW018VlR6gBK5qGrVu34t2LFzFQKi1nWrEcB4o0vo1a+ECVx5mryRJQHNFlDXx/ZeNC7GfTNGHR17L/V1QVgueR9kjadO+6LuECBjA2NASR0poahrFykJ7u7oIgQKatkswIGdl7tHjQumrbsTxq8En5APazbVlo1GpQGaUssFwbp0JkPM8jm8lg644dGN7Ag+v3Ej2jXQW5fB6qpmFuamqZw1dRmhJFsihi89gYbt68ifcuXcKDtG7LYmH2czwDy3McJElqkvfwgwCe68J23Yi8PGpdDMNlnVkQzmOPtiUy150DydqKmQx0XUe9XsfM9DTmZmbAg/Rfu7QrStU0pKhOEFMlYOfKdvNOiPqs2bUlZHgG0v1YAAAJV0lEQVQT30df7/k+Zmn2V5bliGbWdV3STywIyGaz6C+VMDo+Dn2DUsN8GOBWmcjobr7qE4AgCDBfLqO2sAARWG5iiGFqehrHjx/H4cOHUSgUACBKXq0l+nLog8uBNCBwdBqGo8bJ5kZt215RUwaoFqzj4PbEBG6+/z527NiBdCYDz3WXGxroa2VZhqooUDWNJKMouXtTjNtyfszoEnmMW8CG1ePthq7r4vadO6hUq1BUFRJ1uZkUSUrTIMsy+oeG0D84+EmNXdtWCXtGu0bU63XMz87CN00ostwkvhWEIS5duoSrV6/i6NGjJBsahk27ThTvtRhPHD7V++k0SG7ZNsx6Hbl8nmjvBgFsyyJJoTDEtatXsbS0hP00S6yn02hQSRKe6s1alkVYN2g8HQKRNpBMs7yiIBDXnpasBJq0YjtiO3ieRzLpjkNqsr4Pj/5cq9VQbzSgqSqKxSI0VYWWSkUZ5VQ6jeHNmz8xddc26BntvYTrulhcXESjWkXgOJBpxw/ryT1+7BhCjsMj+/aR7qROAwWINQ/Earie7yOkFCzsdwAigSqPPvyKokTjhQznz56FKIo4cOAAYcjguGhCp2GasC0rMmTWGmlRyhyWhGKJs4STjXZLLtY40jQ8QGP9eIsjTxcApsKnp1IYHBqKFrEwJIJZpaEhZDaACNZHgJ7RfhhwqC5rfWkJvm1DooLPfhDg+9//PjZt2oTNmzcT4rNVDDeOeHml6eGn9VLX82BZFqqVCmn3o1o5Rq2GU6dPY3hkBHv37In6eFVKIM6+TMdx0KjXwfM8VE2DLElRwqz1efCoLi0T7bIcJ5Jaaa1bx+vLbMSOaesycvFarQZVUVDs64ten0qn0T88TPimemDoGe2HCbbrVRcW4NHpGMuy8NZbb6E0MIBtW7ZAb2kPXA0s8eRTojKXupqskZ7jOPzwhz/ESy++iD/+4z/G1PQ0ZmZm8Ohjj2GMCm3Z1DgzdPqH1T3BEUlI1mt869YtfOMb38Av/dIv4bPPPdfk0kdDB7Fkl0+TZN2AsSnWDQMNqmeUy+cJ7Womg/6BAejrXMT5Y0Jbo+1lj+8BRFFEoVBALpeDaZowqlUIhoEDBw7g7JkzOFerYdv27VBkGRptaoiyyrG/fVrm8T0PHjVWgK6cIWVooI30TLqRFwT8+Cc/wcMPPYTPfe5zkEQRJ06cwMX33sP01BSmZ2YwOzODQ089ha985SvROQuCgGwmA8u2sXlsDCNDQzh75gw++9xzK6hk2DBDRBHTEqcngg4DNBoNWKaJIAyRyWRQLBaR7+tDvlhsok3toXv0jPYegud56LoeUZ26rouBsTG89vLLuHTpEraOj8M0TVLqkeUVbYPMRWV10pCWY1jjAmJGUy6XMTE5CZ7nceCJJ7B927boOC+88AImb99Gqb8/WTM3Nkqn0kVg165dOHv2LGZnZ5HP5yFKUtO8b9M5xhgl2NBASF34EKTLybQsMhzguhBlGf0DAxjdvLlXurkH6BnthwhJktA/OIj/6+d+Dq+9/DLeOn0a2zZtwujICGn1ozEwU61vHU5g5R0G27Lw/q1beP/mTQQhUTLgOG6Ffu0v/uIvIpPNIp1OY+rOHfzZn/3ZypPjuCipxfM8HnnsMbz24x/j4sWL2LN3L6nr0nniiLeKuuwMTfO6VP3dptKcnuNA1jSUBgYwODz8iewR/rDQM9qPABzH4chnPoMnDh7EW2++idfffBPDpRLGRkejaRxFVSHRcb7ofSBUMJVKBbfefx+zs7MYHR3F/v37USwW8f/9z/8ZlXvY6wMAD+/ejRrlmuI4LrG7KqJVpRniPbt3g+M4nD9/HocOHYqG123HIaN+lGWCdUUxV9mjSTGbEqj7ngc9k8HA2BiKfX0RB1cP9w69u/kRQtd1HH32WRx++mmcPXsWZ0+dQo3SuqZ1HXoqBZWKVpumCbNeJ51Luo6x0VE8/vjjK5JZrDwTH6R3XTfSiQXHkdG9ll2bgRm9LMvYs2cPzpw9G7n5GiW5s6m7GwYBApq9ZkkyjuPAiyK0VAqariOTzaJQLCKVSm0YZfWNhp7RfgyQJAlPPPEEnnjiiSi7Oj8/j5mZGSwuLqKkKFBlGZokQaQxLZusaSVMc2w76k5inUMWHYTvliOJGe7jjz+OU6dO4d133yUuMouvZZnUhl0XvChCzWQgKwo0Gr9rmrY8NNDC39TDvUfPaD9mcBwHTdMwNjaGsbExAKROy+JDs16HSSdhzHodAe1okgSBdEE5DmHmbzSQ0XWYtMMpFSMxZ+4xM/j438Byf/OePXsgyzJOnjqFzePjZAemg+nZTAbpbBYabe5vJYjr4aNDz2jXIXgqlaGqaqSE4NFMbKNeh2NZpEHCcWCYJjhBQKVaRbVWQ+j7kGWZyGJSw2fk30attqIXmKOzrzzPI9vXh8LgIH742mv4jf/4H0kfsK5DFMW2xGo9fPToGe0GAHM7FcpMAZAd1AkCnLt4EcPj4ygUCrAsC1ysZTEIAly7fRtnL1/G2I4dGBwfb3JfIxYNVlYSBFy9fh1BEGCsNwa3btEz2g0KZniO40BRFAyw4fsWZDIZzMzMwHactq9huH79Os6fP48/+IM/uOfn28O9wydy5qmHZHznO98BAHz+85//mM+kh07oGW0PEb7zne9geHgYBw4c+LhPpYcO6LnH9yFeeOEFvPDCCwAIvzEAHDt2DL/yK78CAOjv78df/MVfNL1nYWEBr7/+On7913+9l3Ba5+gZ7X2IM2fO4Fvf+lbT/12/fh3Xr18HAIyPj68w2n/913+F7/s913gDoOce34f4kz/5k2iwIOnPzZs3V7znO9/5DtLpND7zmc989Cfcw5rQM9oeYFkWXnrpJfz0T/90E31OD+sTPaPtAWfPnsWOHTvwC7/wCx/3qfTQBXoxbQ84ePAgzpw583GfRg9dome0GxhHjx4FgN6s6icMPY6oHnpYn2hbd+vFtD30sMHQM9oeethg6BltDz1sMPSMtoceNhh6RttDDxsMPaPtoYcNhp7R9tDDBkPPaHvoYYOhZ7Q99LDB0DPaHnrYYOgZbQ89bDD0jLaHHjYYekbbQw8bDD2j7aGHDYae0fbQwwZDz2h76GGDYTXmih4Bbg89rDP0dtoeethg6BltDz1sMPSMtoceNhh6RttDDxsMPaPtoYcNhp7R9tDDBsP/AalCZ4SWhZvKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.tools.visualization import plot_bloch_multivector\n",
    "backend = BasicAer.get_backend('statevector_simulator')\n",
    "circuit = QuantumCircuit(q, c)\n",
    "circuit.iden(q[0])\n",
    "job = execute(circuit, backend)\n",
    "state = job.result().get_statevector(circuit)\n",
    "print(\"Initial state\")\n",
    "plot_bloch_multivector(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the Hadamard gate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After a Hadamard gate\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.h(q[0])\n",
    "job = execute(circuit, backend)\n",
    "state = job.result().get_statevector(circuit)\n",
    "print(\"After a Hadamard gate\")\n",
    "plot_bloch_multivector(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The third way of visualizing what happens is plotting the statistics of measurement results. Arguably, this is the most important for practical applications and debugging. This visualization needs the `qasm_simulator` backend."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T19:31:24.455598Z",
     "start_time": "2018-11-19T19:31:24.109562Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial state statistics\n",
      "Statistics if we apply a Hadamard gate\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.tools.visualization import plot_histogram\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "q = QuantumRegister(1)\n",
    "c = ClassicalRegister(1)\n",
    "circuit = QuantumCircuit(q, c)\n",
    "circuit.measure(q[0], c[0])\n",
    "job = execute(circuit, backend, shots=1000)\n",
    "print(\"Initial state statistics\")\n",
    "plot_histogram(job.result().get_counts(circuit))\n",
    "circuit = QuantumCircuit(q, c)\n",
    "circuit.h(q[0])\n",
    "circuit.measure(q[0], c[0])\n",
    "job = execute(circuit, backend, shots=1000)\n",
    "print(\"Statistics if we apply a Hadamard gate\")\n",
    "plot_histogram(job.result().get_counts(circuit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the 'perfect' nature of the simulator is reflected again in getting all 0s for the initial state, and a distribution very close to uniform after applying the Hadamard gate. In a longer circuit on real quantum hardware, these statistics would be heavily affected by noise."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
